UC-NRLF 


UNIVERSITY  OF   CALIFORNIA 

LIBRARY 

OF  THE 

DEPARTMENT   OP   PHYSIC'S > 


Received *J£>..:........ / 


Accessions  No.  .......    ./  ......       Book  No. 


GIFT  OF 


LOWER  DIVISION 


PRACTICAL  MEASUREMENTS 


IN 


MAGNETISM  AND  ELECTRICITY 


BY 


GEORGE   A.    HOADLEY,   A.M.,  C.E, 

PROFESSOR   OF   PHYSICS   IN    SWARTHMORE   COLLEGE 
AUTHOR   OF    "A    BRIEF   COURSE   IN    PHYSICS" 


NEW  YORK-:- CINCINNATI.:- CHICAGO 

AMERICAN    BOOK     COMPANY 


I 


COPYRIGHT,  1904,  BY 
GEORGE   A.   HOADLEY. 

ENTERED  AT  STATIONERS'  HALL,  LONDON. 


HOADLEY'S  MEAS. 
W.  P.   I 


-. 


INTRODUCTORY 

IN  preparing  this  book,  the  purpose  has  been  to  meet 
the  requirements  of  students  in  the  scientific  courses 
in  high,  preparatory,  and  manual  training  schools,  and 
in  the  introduction  to  more  advanced  work  in  college,  as 
well  as  those  of  the  practical  man  who  wishes  to  become 
familiar  with  the  foundation  principles  of  the  subject. 
The  greatest  benefit  that  can  be  derived  from  experi- 
mental work  is  that  obtained  from  the  careful  and  pains- 
taking observation  of  the  experimenter  ;  for  this  reason 
the  directions  given  for  the  experiments  are  in  outline, 
rather  than  in  detail. 

The  student  who  makes  these  experiments  should  keep 
careful  notes,  adding  to  the  apparatus  recommended  any- 
thing that  may  seem  desirable,  varying  the  manipulation, 
and  drawing  such  conclusions  as  the  experiment  teaches. 
He  should  also  keep  a  full  set  of  notes  on  observations 
made.  The  accuracy  and  fullness  of  these  notes  will  be 
an  index  of  the  benefit  that  he  is  receiving  from  the  work. 

No  attempt  has  been  made  to  cover  more  than  a  small 
part  of  the  field;  but  the  belief  is  entertained  that  a 
thorough  familiarity  with  the  principles  and  experiments 
outlined  in  this  book  will  provide  a  good  foundation  for 
a  more  extended  study,  or  for  the  practical  application  of 
these  principles  to  the  requirements  of  practice. 

328841 


CONTENTS 

PAGE 

MAGNETISM  .        .        .        .        ...        .  .        .        .  5 

ELECTRICITY         ,     „        .        „        ...  .,..._—•      ,  .  35 

Galvanometers        ,        .        .        .        .        .  .        .  46 

Batteries          .        .        .        .                .        .  ...  54 

Resistance       .        .         .    •     .        .        .        .  .        ;        .  60 

Current,  etc.    .        ,        ..        .        .        .  ,        ,        .  87 

APPENDIX  : 

Resistance  of  pure  copper  wire       .        .        .  .     "   . '      .  105 

Relative  resistance  of  different  substances     ....  106 

Relative  properties  of  copper  and  aluminum  .        .        .  107 

Equivalents    ....'..        .'  .        .        .  107 

Answers  to  problems       .        .         .        *        .  .        .         .  108 

INDEX 109 


CHAPTER   I 
MAGNETISM 

1.  Magnetic  and  Non-magnetic  Substances.  —  Substances 
may  be  divided  into  classes,  according  to  their  action  when 
in  the  presence  of  a  strong  bar  magnet.  Those  that  cling 
to  the  magnet  are  called  magnetic  substances;  those  that 
do  not  are  called  non-magnetic. 

EXPERIMKNT  1.  —  To  separate  magnetic  from  non-magnetic  sub- 
stances. 

Apparatus.  —  A  strong  bar  magnet ;  twenty  or  thirty  objects  made 
of    different    substances,    such    as    screws, 
matches,  copper  rivets,  bicycle  balls,  etc. 


Manipulation.  —  Place  these  objects  upon 


MAGNETIC 


Nails 


NON-MAGNETIC 


Matches 


a  table  and  touch  each  of  them  with  the 
end  of  the  bar  magnet. 

Make   a   table   like   the   one   suggested, 
classifying  the   different   articles   as   mag- 
netic or  non-magnetic.     Are  any  of  the  magnetic  substances  non- 
metallic?     Are  all  the  metals  magnetic? 

A  further  examination  of  different  substances  will  prove 
that,  besides  iron  and  steel,  nickel  and  cobalt  are  magnetic. 
This  may.  be  shown  by  bringing  the  end  of  a  bar  magnet 
in  contact  with  these  metals  or  some  of  their  ores.  Of 
the  ores  of  iron,  some,  like  magnetite,  are  magnetic,  while 
others,  like  sphalerite,  are  not.  If,  however,  a  piece  of 
sphalerite  is  heated  under  a  blowpipe,  it  becomes  magnetic. 

5 


MAGNETISM 


^  -'•    • '  f  1  r    --1"'    . 

2.  The  Poles  of  a  Magnet.  —  Every  bar  magnet  exerts  a 
greater  attractive  power  near  its  ends  than  at  any  other 
point.  These  points  of  maximum  attraction  are  called 
the  poles  of  the  magnet. 

EXPERIMENT  2.  —  To  locate  the  poles  of  a  bar  magnet. 

Apparatus.  —  A  bar  magnet  and  a  box  of  small  nails  or  tacks. 

Manipulation.  —  Pour  the  nails  upon  a  table,  dip  one  end  of  the 
magnet  into  them,  and  then  raise  it  vertically.  Do  the  same  with  the 
other  end.  Spread  the  nails  out  in  a  line  as  long  as  the  magnet,  lay 
the  magnet  down  upon  its  side  in  the  nails,  and  then  raise  it  vertically 
as  in  the  figure. 


FIG.  1 


The  position  of  the  poles  is  indicated  by  the  number  of  nails  that 
cling  to  the  magnet  at  different  points.  Locate  as  definitely  as  you 
can  the  distance  of  each  pole  from  the  end. 

3.   Names  of  the  Magnetic  Poles.  —  EXPERIMENT  3.  — To 

name  the  poles  of  a  magnet. 

Apparatus.  —  A  small  bar  magnet ;  silk  thread. 

Manipulation.  —  Suspend  the  magnet  from  the  middle  by  the  thread 
in  such  a  manner  that  it  can  swing  freely  in  a  horizontal  plane,  and 
let  it  come  to  rest. 

A  magnet  suspended  or  supported  in  this  way  constitutes 
a  magnetic  needle. 


THE  MUTUAL  ACTION  OF  MAGNETS 


FIG.  2 


The  line  in  which  it  finally  comes  to  rest  is  called  the 
magnetic  meridian.  The  end  of  the  needle  that  points 
to  the  magnetic  north  is 
called  the  north,  the  JV,  or 
the  +  pole,  and  the  other  _^Er/c  ^ 
the  south,  the  $,  or  the 
—  pole. 

The     strictly     accurate, 
though  less  convenient,  names  would  be  the  north-seeking 
pole  and  the  south-  seeking  pole. 

4.    The  Mutual  Action  of  Magnets.  —  EXPERIMENT  4.  —  To 

investigate  the  law  of  mutual  action. 

Apparatus.  —  The  bar  magnet  used  in  Experiment  3  ;  also  a  small 
magnetic  needle. 

Manipulation.  —  Holding  the  magnet  by  the  S  end,  bring  the  N 
end  near  the  TV  end  of  the  needle  after  it  has  come  to  rest.  Bring  it 
near  the  &  end.  Reverse  the  magnet  and  repeat  both  tests. 

From  the  results  obtained  formulate  a  law  that  shall  state  the 
mutual  action  of  like  and  of  unlike  poles.  This  "law  of  mutual 
action"  is  an  extremely  important  one  and  explains  many  of  the 
phenomena  that  are  observed  in  magnetism. 


5.  The  Poles  of  a  Horseshoe  Magnet.  - 
When  a  bar  magnet  is  bent  in  the  middle 
and  its  ends  are  brought  near 
each  other,  it  is  called  a  horseshoe 
magnet.  A  piece  of  soft  iron 
placed  across  the  ends  is  called 
the  armature.  If  the  magnet  is 
formed  of  a  single  bar,  it  is  a 
simple  magnet  (Fig.  3)  ;  but 
if  it  is  made  up  of  a  number  of 
thin  magnets  fastened  together,  it  is  a 
compound  horseshoe  magnet  (Fig.  4). 


FIG.  3 


FIG 


8  MAGNETISM 

EXPERIMENT  5.  —  To  locate  the  poles  of  a  horseshoe  magnet. 

Apparatus.  —  A  horseshoe  magnet;  a  magnetic  needle. 

Manipulation.  —  Bring  the  different  parts  of  the  magnet  near  the 
N  end  of  the  needle  and  observe  the  effect. 

Name  the  poles  of  the  magnet  by  applying  the  law  that  was  deter- 
mined in  the  preceding  experiment. 

6.  Magnetic  Induction.  —  EXPERIMENT  6.  — To  show  the  in- 
ductive effect  of  a  bar  magnet. 

Apparatus.  —  A  long  bar  magnet ;  a  soft  iron  rod  3  or  4  in.  long ; 
and  iron  filings. 

Manipulation.  —  Bring  one  end  of  the  soft  iron  rod  near  the  end  of 
the  magnet,  and  while  it  is  in  that  position  put  the  other  end  of  the 
rod  into  the  iron  filings.  Raise  the  rod  from  the  filings  and  then 
slowly  move  the  magnet  away  from  the  rod. 

This  changing  of  an  iron  rod  into  a  magnet  in  the  presence  of  a 
magnet  is  the  result  of  what  is  known  as  magnetic  induction.  If  the 
experiment  is  extended  by  placing  a  succession  of  iron  rods  in  the 

_i_ 
•i-    -     -h     -      +  -     +    - 

FlGr  5 

axis  of  the  magnet  as  in  Fig.  5,  an  examination  of  the  polarity  of 
each  will  show  that  it  is  as  marked  in  the  figure.  The  position  of 
the  poles  is  determined  by  the  law  of  mutual  action. 

7.  Inductive  Action  of  the  Earth.  — The  fact  that  a 
magnetic  needle  will  always  come  to  rest  in  a  fixed  direc- 
tion shows  that  the  earth  itself  acts  like  a  great  magnet. 
The  line  in  which  the  needle  comes  to  rest  is  called,  as 
has  been  said,  the  magnetic  meridian,  and  the  points  toward 
which  all  the  different  magnetic  meridians  converge  are 
called  the  magnetic  poles  of  the  earth. 

EXPERIMENT  7.  —  To  show  the  inductive  action  of  the  earth's 
magnetism. 

Apparatus.  —  A  bar  of  soft  iron  about  3  ft.  long  and  an  inch  in 
diameter ;  a  magnetic  needle  mounted  on  a  stand, 


MAGNETIC  INDUCTION  9 

Manipulation.  —  After  the  needle  has  come  to  rest,  bring  one  end 
of  the  iron  bar  near  the  N  end  of  the  needle,  keeping  the  bar  in  the 
horizontal  plane  and  in  an  east-and-west  line,  as  in  Fig.  6.  Make  the 
same  experiment  with  each  end 
of  the  bar  upon  each  end  of  the 
needle.  If  the  bar  is  of  soft 
iron,  attraction  should  take  place 
in  each  case.  Now  bring  the  iron 
bar  into  the  magnetic  meridian, 
raise  the  southern  end  until  the 
bar  makes  an  angle  of  about 
70  degrees  with  the  horizon,  and  *r 

bring    its    lower   end   near   one  "  ^ 

side  of  the  N  end  of  the  needle. 
Make   the  same  experiment  on 

the  S  end  of  the  needle.    Reverse    /w  FIG.  6 

the  bar  and  repeat. 

This  experiment  if  carefully  made  is  most  striking  and  instructive, 
its  results  showing  that  the  inductive  action  of  the  earth  determines 
the  polarity  of  the  bar  in  both  positions. 

EXPERIMENT  8.  —  An  extension  of  Experiment  7. 

Apparatus.  —  The  iron  bar  and  needle  used  in  Experiment  7,  and 
a  hammer. 

Manipulation.  —  Bring  the  bar  into  the  position  in  which  it  produces 
the  greatest  deflection  of  the  needle  and  then  strike  it  two  or  three 
sharp  blows  with  the  hammer.  Hold  it  in  the  horizontal  plane  and  test 
it  for  polarity.  Hold  it  in  the  magnetic  eastand-west  line  and  again 
strike  it  a  few  blows.  Test  it  once  more  for  polarity.  In  making  a 
test  for  polarity  the  only  acceptable  proof  is  repulsion,  not  attraction. 

The  results  of  these  tests  show  that  if  an  iron  bar  is  jarred  mechan- 
ically while  it  is  magnetized  by  induction  it  will  retain  a  certain 
amount  of  magnetism.  If  the  bar  were  of  steel,  it  would  become  a 
permanent  magnet.  The  demagnetization  of  the  iron  bar  that  takes 
place  when  it  is  struck  while  in  the  magnetic  east-and-west  line  is 
possibly  due  to  its  being  magnetized  transversely. 

EXPERIMENT  9.  —  To  test  vertical  iron  rods  for  magnetic 'polarity. 
Apparatus.  —  A  magnetic  needle,  retort  stand,  and  any  vertical  iron 
rods  or  pipes  that  may  be  in  the  laboratory  or  its  vicinity. 


10  MAGNETISM 

Manipulation.  —  Hold  the  needle  near  the  top  of  the  retort  stand 
and  determine  the  polarity.  Lower  the  needle  slowly  until  the  foot  of 
the  stand  is  reached.  Determine  the  polarity  of  the  stand  along  its 
entire  length  and  mark,  on  a  drawing,  the  point  at  which  it  changes. 

An  examination  of  steam  pipes,  iron  fence  posts.,  and  in  fact  any 
iron  or  steel  rods  that  have  stood  for  some  time  in  an  approximately 
vertical  position,  shows  that  they  are  magnetized.  It  also  shows  that 
the  upper  end  of  each  is  a  south  pole  and  that  the  lower  end  is  a 
north  pole.  Why? 

QUESTIONS 

1.  Is  an  ordinary  tin  plate  magnetic  or  non-magnetic?     Why? 

2.  Is  the  pole  of  a  bar  magnet  nearer  the  end  in  a  long,  thin  mag- 
net, or  in  a  short,  thick  one  ? 

3.  Give  illustrations  of  the  mutual  action  of  magnets.     State  the 
law. 

4.  Make  a  drawing  of  a  horseshoe  magnet  with  its  armature  nearly 
touching  the  ends  of  the  magnet.     Mark  the  polarity  of  both  the 
magnet  and  the  armature. 

5.  -What  kind  of  magnetic  polarity  has  the  north  magnetic  pole  of 
the  earth  ?     What  two  experiments  prove  it  ? 

6.  Why  are  steel  tools. frequently  found  to  be  magnetized? 

7.  Why  is  attraction  no  proof  of  polarity  ? 

8.  Making  a  Magnetic  Needle.  —  EXPERIMENT  10.  — To  mag- 
netize a  piece  of  steel. 

Apparatus.  —  A  piece  of  watch  spring  or  a  sewing  needle;  a  bar 
magnet ;  and  a  magnetic  needle. 

Manipulation.  —  Straighten  the  watch  spring  by  drawing  it  between 
the  fingers.  Holding  the  spring  firmly  upon  some  flat  surface,  draw 
the  N  end  of  the  magnet  from  the  middle  to  one  end.  Do  this  at  least 
twenty  times.  Draw  the  S  end  of  the  magnet  along  the  other  end  of 
the  spring  an  equal  number  of  times.  Determine  the  polarity  of  the 
spring  by  testing  it  with  the  magnetic  needle. 

State  the  kind  of  polarity  produced  by  drawing  the  N  end  of  a 
magnet  along  one  end  of  a  piece  of  steel. 

9.  Demagnetization.  —  The  demagnetization  of  a  magnet 
may  be  accomplished  in  several  ways,  one  of  which  is 
shown  in  the  following  experiment. 


DEM A  GNETIZA  T1ON 


11 


EXPERIMENT  11.  —  To  demagnetize  a  magnet  by  heat. 

Apparatus.  —  The  magnetic  needle  made  in  Experiment  10  ;  a  cop- 
per wire  about  6  in.  long;  a  Bunsen  burner;  and  a  magnetic  needle. 

Manipulation.  —  Wind  one  end  of  the  copper  wire  around  the  middle 
of  the  watch-spring  needle  and  hold  the  needle  in  the  flarne  of  the 
Bunsen  burner  until  it  is  white  hot.  Remove  it  from  the  flame,  allow 
it  to  cool,  and  examine  it  for  polarity.  Heat  it  again,  plunge  it  into 
water,  and  magnetize  it  again  as  in  Experiment  10. 

Conclusion.  —  The  increased  rate  of  molecular  vibration  due  to  the 
heating  of  the  needle  changes  it  from  a  magnet  to  a  magnetic  sub- 
stance, or  demagnetizes  it.  Compare  this  result  with  that  obtained 
by  striking  the  iron  bar  in  Experiment  8. 

10.  The  Effect  of  High  Temperatures  upon  Magnets.  — 

EXPERIMENT  12.  —  An  extension  of  Experiment  11. 

Apparatus.  —  A  bar  magnet ;  a  knitting-needle  magnet ;  a  support- 
ing stand  ;  and  a  Bunsen  burner. 

Manipulation. — 
Suspend  the  knitting- 
needle  magnet  by  a 
wire  in  such  a  way 
that  it  will  diverge 
some  degrees  from 
the  magnetic  merid- 
ian. This  can  be 
done  by  twisting  the 
wire  suspension  at 
the  top.  Fix  the  bar 
magnet  as  shown  in 
the  figure,  when  the 
attraction  of  the 
magnet  for  the  needle 
will  overcome  the  tor- 
sion of  the  wire  and 
bring  the  unlike  ends 
in  contact  with  each 

other.  Now  apply  the  flarne  of  the  Bunsen  burner  to  the  end  of 
the  needle  that  is  nearest  the  magnet,  and  when  this  begins  to  get  red 
hot  the  needle  will  swing  back  away  from  contact  with  the  magnet. 


12  MAGNETISM 

Experiment  has  proved  that  the  temperature  at  which 
this  result  takes  place,  is  about  785°  Centigrade.  This 
means  that  at  this  temperature  and  above,  iron  is  a  non- 
magnetic substance. 

11.  Magnetic  Lines  of  Force.  —  From  the  results  of  the 
experiment  on  induction  it  is  evident  that  the  space  sur- 
rounding a  magnet  differs  from  the  space  surrounding  a 
bar  of  iron.  Around  the  magnet  there  is  what  is  called  a 
magnetic  field,  and  through  this  there  extend  lines  of  mag- 
netic force.  These  lines  of  force  are  closed  circuits  passing 
externally  from  the  north  to  the  south  pole,  and  internally 
from  the  south  to  the  north  pole.  They  pass  more  readily 
through  magnetic  substances  than  through  non-magnetic ; 
constantly  tend  to  shorten  their  paths  like  stretched  rub- 
ber bands  ;  and,  if  parallel  and  in  the  same  direction,  repel 
each  other. 

In  direction  each  line  of  force  is  the  path  along  which 
an  isolated  north  pole  would  be  repelled  by  the  magnet, 
were  such  an  isolation  possible. 

EXPERIMENT  13.  —  To  determine  the  direction  of  the  lines  of  force. 

Apparatus.  —  A  bar  magnet ;  a  very  short  magnetic  needle ;  a  sheet 
of  paper  ;  window  glass ;  iron  filings ;  and  a  sieve  made  of  fine  woven 
wire  or  of  thin  muslin. 

Manipulation.  —  Place  the  bar  magnet  on  its  side  upon  a  table  and 
over  it  lay  a  sheet  of  paper.  Lay  the  sheet  of  glass  over  this  and  sift 
a  light  coat  of  iron  filings  over  its  upper  surface.  Rap  the  glass  lightly 
with  a  lead  pencil,  and  the  filings  will  arrange  themselves  in  curves 
that  indicate  the  paths  of  the  lines  of  force  and  the  comparative  in- 
tensity of  the  magnetic  field.  Determine  the  direction  of  the  lines  of 
force  by  suspending  at  different  points  above  the  curves  a  very  short 
magnetic  needle  and  observing  the  direction  in  which  the  north  pole 
is  repelled. 

The  most  satisfactory  record  of  these  curves  can  be  made  by  carry- 
ing out  the  experiment  in  a  dark  room,  using  the  film  surface  of  a 


MAGNETIC  LINES   OF  FORCE 


13 


photographic  dry  plate  as  a  support  for  the  filings.  When  the  desired 
curves  are  obtained,  the  plate  is  exposed  by  burning  a  match,  held  a 
foot  or  more  above  it,  and  is  then  developed  in  the  usual  way.  A 
slow  plate  is  best  for  this  purpose,  and  the  prints  are  much  more 
accurate  than  drawings,  as  is  shown  in  Fig.  8. 


FIG.  8 

Let  negatives  and  prints  of  the  following  fields  be  made : 

1.  Side  of  bar  magnet ; 

2.  End  of  bar  magnet; 

3.  Side  of  horseshoe  magnet ; 

4.  End  of  horseshoe  magnet ; 

5.  Two  horseshoe  magnets,  one  inch  apart,  like  poles  opposite ; 

6.  Two  horseshoe  magnets,  one  inch  apart,  unlike  poles  opposite; 

7.  Horseshoe  and  bar  magnet,  one  inch  apart ; 

8.  Bar  magnet  and  iron  bar,  one  inch  apart,  showing  induction ; 

9.  Field  devised  by  the  student ; 
10.  Field  devised  by  the  student 


14  MAGNETISM 

12.  Geometrical  Construction  of  the  Direction  of  Lines  of 
Force. — A  very  important  equation,  which  expresses  the 
value  of  the  force  between  two  bodies  that  act  mutually 

ff 
upon  each  other,  is  F  =  *~.     In  the  case  of  two  magnets 

this  expression  takes  the  form  F  =  ±  ~T^  in  which  m  and 

m'  are  the  strengths  of  two  magnetic  poles,  and  d  is  the 
distance  between  them.  The  sign  +  is  used  when  there 
is  mutual  repulsion,  as  between  like  poles;  the  sign  — 
when  there  is  mutual  attraction,  as  between  unlike  poles. 
The  application  of  this  equation  to  the  geometrical  con- 
struction of  the  direction  of  lines  of  force  is  as  follows: 

Let  NS  (Fig.  9)  represent  a  long,  thin  magnet.  Let  A  be  the  mid- 
dle of  a  small  magnetic  needle  placed  8  in.  from  S  and  12  in.  from  N. 
What  position  will  the  needle  assume  when  it  comes  to  rest  ? 


N 

FIG.  9 


Suppose  the  poles  of  the  magnet  NS  to  be  12  in.  apart,  and  that 
ns  is  so  short  that  its  length  may  be  disregarded.  Let  50  represent  the 
magnetic  strength  of  N  and  of  S,  and  3  that  of  n  and  of  s.  There  will 


THE  EFFECT  OF  BREAKING  A   MAGNET  15 

50  x  3 
be  two  forces  acting  upon  n,  one  of ^  acting  from  N  toward  A, 

and  one  of  —    *  '  acting  from  A  toward  S ;  hence  we  can  write : 

Repulsion  of  N  :  Attraction  of  S  : :  —  :  — 

144      64 

Repulsion  of  N  :  Attraction  of  S  ::     64  :  144 
Repulsion  of  N  :  Attraction  of  S  : :      4  :       9 

To  find  the  position  of  the  needle,  lay  off  on  NA  prolonged,  and 
on  AS,  distances  AB  and  AC  proportional  respectively  to  4  and  9. 
Complete  the  parallelogram  ABDC,  and  the  diagonal  AD  will  be  the 
position  of  the  half  needle  An,  considered  independently.  But  a 
similar  construction  would  show  the  position  of  the  other  half  of  the 
needle  As  to  be  the  prolongation  of  nA  (let  the  student  prove  this)  ; 
hence  no  further  construction  is  necessary.  The  needle  ns  is  tangent 
to  the  direction  of  the  line  of  force  at  the  point  A.  The  position  of 
other  tangent  lines  may  be  found  by  selecting  other  values  for  AN  and 
AS  and  constructing  the  position  of  the  needle  as  before.  Let  the 
position  be  found  at  the  following  distances : 

1.  AN  14,  AS  6. 

2.  AN  9,  AS  9. 

3.  AN  4,  AS  10. 

4.  AN  2,  AS  15. 

Verification.  —  Upon  the  drawing  made  in  the  foregoing  construc- 
tion, lay  a  magnet  with  its  poles  12  in.  apart  and  just  over  the  poles  of 
the  drawing.  Place  a  short  magnetic  needle  at  the  point  A  and  turn 
the  board  until  the  needle  coincides  with  n.s,  when  the  needle  will 
be  found  to  be  in  the  magnetic  meridian.  Why? 

NOTE.  —  For  convenience  in  the  verification  it  will  be  well  to  make 
the  distance  NS  in  the  drawing  equal  to  the  distance  between  the 
poles  of  some  magnet  that  you  have  used. 

13.   The  Effect  of  Breaking  a  Magnet.  —  EXPERIMENT  14. — 

To  show  that  each  piece  of  a  broken  magnet  is  polarized. 

Apparatus.  —  A  knitting  needle  ;  a  magnet ;  a  magnetic  needle  ;  iron 
filings;  and  a  three-cornered  file. 

Manipulation.  —  File  a  notch  in  the  middle  of  the  knitting  needle 
and  break  it  in  two.  Magneti/e  one  half  of  it  as  in  Experiment  10 


16  MAGNETISM 

so  that  the  point  will  be  +.  Test  it  for  magnetism  with  the  filings 
and  determine  its  polarity  with  the  needle.  File  a  notch  in  the 
middle  of  the  half-needle  magnet  and  break  again.  Test  as  before. 
Break  the  pointed  end  in  two  and  test  again.  Carry  the  experiment 
as  far  as  possible,  or  until  you  can  not  break  the  needle  again. 


+     -    4-      -     4- 


FIG.  10 


The  results  obtained,  shown  in  Fig.  10,  suggest  the  results  of 
induction  in  Experiment  6.  Can  you  break  off  a  piece  of  the  magnet 
so  short  that  it  will  not  be  polarized  ? 

14.  Explanation  of  Induction.  —  Since  the  shortest  piece 
that  we  can  obtain  by  breaking  a  magnet  is  found  to  be 
polarized,  the  hypothesis  has  been  made  that  each  mole- 
cule of  a  magnetic  substance  is  a  magnet.  The  difference 
between  a  piece  of  soft  iron  and  a  steel  magnet  is  that  in 
the  magnet  the  molecular  magnets  are  practically  parallel 
to  one  another  and  all  in  the  same  direction,  while  in  the 
soft  iron  they  are  in  positions  that  are  determined  by 
their  mutual  attractions  and  repulsions.  If  a  strong  bar 
magnet  is  brought  near  a  soft  iron  bar,  the  molecular 
magnets  of  which  the  bar  is  composed  are  drawn  around 
into  lines  that  are  practically  parallel  in  direction,  and  we 
say  that  the  iron  is  polarized  by  induction. 

EXPERIMENT  15.  —  To  represent  induction  in  soft  iron. 

Apparatus.  —  Watch  spring;  bar  magnet;  pins;  sheet  of  lead; 
steel  punch;  Bunsen  burner;  wire;  and  hammer. 

Manipulation.  —  Break  from  the  watch  spring  twenty  or  more 
pieces  each  an  inch  long,  heat  them  in  the  Bunsen  flame,  and  make 
a  slight  depression  in  the  middle  of  one  side  of  each  with  the  punch. 
Cut  from  the  sheet  of  lead  twenty  or  more  disks  each  an  inch  in 
diameter  and  drive  a  pin  through  the  middle  of  each.  Harden  the 


EXPLANATION   OF  INDUCTION 


17 


springs  by  heating  them  to  a  red  heat  and  plunging  them  into  cold 

water.     Magnetize  and  mount  each  on  one  of  the  pins  as  a  stand 

(Fig.  11).     Place  them  upon  a  table,  symmetrically  arranged  in  the 

form  of  a  long  rectangle.     Observe  the  position  taken 

by  each  and  make  a  sketch  of  the  group.     Now  bring 

one  end  of  a  bar  magnet  near  one  end  of  the  rectangle, 

keeping  the  axis  of  the  magnet  in  the  direction  of  the 

length  of  the  rectangle.     Observe  the  change  in  the 

directions  of  the  needles,  and  after  they  have  come  to 

rest  sketch  the  group  again. 

Figure  12   represents  such  positions  as  the  small 
needles  will  assume  when  they  come  to  rest  under  the 


FIG.  11 


FIG.  12 


influence  of  their  mutual  at- 
tractions and  repulsions 
alone.  In  this  condition 
they  represent  the  molecules 
of  soft  iron  when  they  neutral- 


ize one  another  and  exert  no  magnetic  force  as  a  whole.  If,  however, 
a  strong  bar  magnet  is  brought  near  the  small  magnets,  their  mutual 
action  is  overpowered,  and  the  result  is  shown  in  Fig.  13. 


FIG.  13 

In  this  position  they  represent  the  molecules  of  an  iron  bar  polar- 
ized by  induction. 

Instead  of  the  form  of  needles  described  above,  the  pieces  of  watch 
spring  may  be  magnetized  and  then  placed  upon  a  piece  of  glass, 
resting  on  their  convex  sides.  It  will  be  difficult,  however,  to  pre- 
vent their  coming  in  contact  with  one  another.  A  better  arrange- 
ment is  to  use  a  number  of  small  magnetic  compasses  which  can 
be  placed  in  any  desired  position. 


15.   The  Lifting  Power  of  a  Magnet.  —  EXPERIMENT  16. — 

To  determine  the  lifting  power  of  a  magnet. 

Apparatus.  —  Single  and  compound  horseshoe  magnets ;  pail ;  sand ; 
and  a  pair  of  scales. 

ELEC.   AND  MAG.  — 2 


18  MAGNETISM 

Manipulation.  —  Fix  the  single  horseshoe  magnet  in  such  a  posi- 
tion that  the  armature  will  hang  vertically  downward.  Suspend  the 
pail  from  the  armature  and  pour  sand  into  it  until  the  armature  is 
pulled  from  the  magnet.  Weigh  the  armature,  pail,  and  sand,  and 
make  a  record  of  the  weight.  Make  the  experiment  three  times  and 
take  the  average  of  the  weights  for  the  lifting  power  of  the  magnet. 
Suspend  the  pail  from  the  armature  of  the  same  magnet  and  pour 
into  it  almost  as  much  sand  as  was  .supported  in  the  first  experiment. 
Leave  it  suspended  for  an  hour ;  at  the  end  of  that  time  pour  in 
a  little  more  sand,  and  repeat  this  at  the  end  of  each  hour  until  the 
armature  is  pulled  off.  Find  the  weight  and  compare  it  with  that 
supported  in  the  first  experiment.  Suspend  the  pail  again  and  pour 
in  sand  until  the  armature  is  again  pulled  off.  Weigh  the  load  and 
again  compare  with  the  first.  Weigh  the  magnet  and  compare  its 
weight  with  that  of  its  maximum  load. 

The  results  show  that  by  gradually  building  up  the  load  on  a 
magnet  its  lifting  power  is  increased.  They  also  show  that  the  in- 
crease is  not  permanent. 

Make  the  same  experiments  with  the  compound  magnet. 

Is  the  lifting  power  of  a  compound  magnet  formed  of  ten  single 
magnets  of  equal  strength,  ten  times  as  great  as  the  lifting  power  of 
one  of  them  ?  Give  the  reason  for  your  answer. 

16.   The  Action  of  the  Earth  upon  a  Magnetic  Needle.  - 
EXPERIMENT  17.  —  To  show  that  the  action  of  the  earth  upon  a  mag- 
netic needle  is  simply  directive. 

Apparatus. —  Beaker  of  water;  sewing  needle;  magnet;  and 
wire. 

Manipulation.  —  Magnetize  the  sewing  needle  in  such  a  manner 
that  its  point  is  a  north  pole.  Draw  it  between  the  fingers  and  lay  it 
carefully  upon  the  surface  of  the  water,  using  the  wire,  bent  into  a 
loop,  for  that  purpose.  It  will  come  to  rest  in  the  magnetic  meridian. 
Deflect  it  from  that  position  by  bringing  one  end  of  the  magnet  toward 
the  side  of  the  beaker.  Repeat,  and  observe  that  every  time  it  comes 
to  rest  it  simply  turns  into  the  north  and 'south  line  without  moving 
either  to  the  south  or  to  the  north. 

Conclusion.  —  Since  the  needle  moves  neither  to  the  north  nor  to  the 
south,  the  action  of  the  earth  upon  a  magnetic  needle  is  directive  only. 

Bring  a  bar  magnet  near  the  beaker  and  explain  the  action. 


THE  EARTH  S   MAGNETIC  FORCE 


19 


17.  The  Terrestrial  Magnetic  Couple.  —  A  study  of  Fig. 
14  will  show  the  reason  for  the  results  obtained  in  Experi- 
ment 17.     Let  NS  represent  the  magnetic  meridian  and 
ns  a  needle   that  is  deflected  from  it   by  the 

angle  a.     By  the  law  for  the  mutual  action  of 

r,         mm' 

magnets,  the  force  acting  on  n  is  F  = — - , 

and  that  acting  on  s  is  F=  -\ — — ,  in  which   m 

and  m'  are  the  respective  strengths  of  the  north 
pole  of  the  needle  and  of  the  earth.  Since  these 
forces  are  parallel  and  opposite  in  direction, 
they  form  a  mechanical  couple  the  only  effect 
of  which  is  to  turn  the  needle  ns  on  its  axis 
at  0.  There  will  be  a  similar  expression  for 
the  action  between  the  south  pole  of  the  earth 
and  the  needle.  Since  the  distance  is  inde- 
terminate, we  will  call  the  horizontal  effect  of 
the  earth's  magnetism  If.  The  forces  acting 
upon  n  and  s  will  then  be  each  mH.  The  moment  of 
each  force  will  be  mffx  nb,  and  the  total  moment  will  be 
ZmHxnb.  But  nb  =  nOs'u\  a.  Hence  F=  mHx2nO  sin  a. 
Let  I  =  2  nO,  the  length  between  the  poles  of  the  needle  ; 
then  F=mHl  sin  a.  But  ml  is  the  magnetic  moment  of 
the  needle  ;  call  this  M^  and  F  =  MH  sin  a. 

18.  Components  of  the  Earth's  Magnetic  Force.  — EXPERI- 
MENT 18.  —  To  show  the  direction  of  the  earth's  magnetic  force. 

Apparatus.  —  Knitting  needle;  small  cork;  sewing  needle;  and  two 
beakers  of  equal  height. 

Manipulation.  —  Thrust  the  knitting  needle  lengthwise  through  the 
cork  and  thrust  the  sewing  needle  through  at  a  right  angle  to  its 
length  and  close  to  the  knitting  needle.  Support  the  ends  of  the 
sewing  needle  on  the  edges  of  the  beakers,  so  that  it  may  serve  as 
an  axis,  arranging  the  beakers  in  such  positions  that  the  knitting 
needle  will  be  in  the  magnetic  meridian.  Push  the  knitting  needle 


20 


MAGNETISM 


back  and  forth  through  the  cork  until  it  will  balance  in  a  horizontal 
position.  Magnetize  the  knitting  needle  carefully  so  as  not  to  change 
its  position  in  the  cork.  Support  it  on  the  beakers  as  before  arid 
observe  the  position  in  which  it  comes  to  rest. 

The  fact  that  the  needle  no  longer  remains  balanced  horizontally 
after  it  has  been  magnetized  shows  that  the  maximum  directive 
force  of  the  earth  is  not  horizontal. 

Let  AB  (Fig.  15)  represent  the  intensity  and  direction 
of  the  earth's  magnetic  force.  This 
may  be  resolved  into  two  component 
forces,  one  AC  horizontal,  and  the 
other  AD  vertical.  Let  these  forces 
be  represented  by  J,  H,  and  V  respec- 
tively, and  let  a  represent  the  angle 
CAB ;  and  we  may  write 

H=I cos  a; 

F~=Zsin  a. 


The  component  H  is  the  force  that 
determines  the  position  of  all  needles 
moving  in  a  horizontal  plane ;   it  is 
called  the  horizontal  component  of  the  earth's  magnetism. 


FIG.  15 


19.  The  Angle  of  Dip.  The  Dipping 
Needle.  —  The  angle  CAB  in  Fig.  15, 
which  measures  the  inclination  of  the 
earth's  magnetic  force  below  the  hori- 
zontal line  passing  through  the  needle, 
is  called  the  angle  of  dip.  A  con- 
venient and  simple  form  of  dipping 
needle  with  which  the  angle  of  dip 
can  be  determined  at  any  place  is 
shown  in  Fig.  16.  The  axis  of  the 
needle  is  supported  by  braces  attached 


FIG.  16 


THE  ANGLE   OF  DIP 


21 


to  a  graduated  ring  which  is  itself  supported  by  an  axis  at 
a  right  angle  to  the  axis  of  the  needle.  The  semicircular 
arms  which  support  the  axis  of  the  ring  are  mounted  at  the 
top  of  a  vertical  standard  capable  of  rotating  on  its  axis. 
At  the  base  of  the  standard  is  a  horizontal  circle  gradu- 
ated to  degrees.  A  pointer  attached  to  the  standard 
determines  its  position  on  the  graduated  circle.  Three 
leveling  screws  are  provided  in  the  base  of  the  instru- 
ment for  adjustment. 

EXPERIMENT  19.  —  To  determine  the  angle  of  dip. 
Apparatus.  —  Dipping  needle,  and  long  magnetic  needle. 
Manipulation.  —  Set  up  the  magnetic  needle  in  the  middle  of  a 
table  and,  by  sighting  across  the  ends  of  the  needle,  mark  two  points 
in  the  magnetic  meridian,  one  at  each  end  of  the  table.  Remove  the 
needle  and  draw  a  chalk  line  from  one  mark  to  the  other.  Set  np 
the  dipping  needle  in  the  middle  of  this  line  and  turn  the  graduated 
ring  into  the  vertical  plane.  Bring  it  into  the  meridian  by  reference 
to  the  chalk  line  and  turn  the  graduated  circle  at  the  base  of  the 
standard  until  the  pointer  marks  zero.  The  needle  is  now  in  the  posi- 
tion to  give  the  reading  of  the  angle  of  dip.  Read  both  the  upper 
and  the  lower  end  of  the  needle.  Turn  the  ring  through  180  degrees 
and  read  again.  Turn  the  standard  through  180  degrees  and  take  four 
readings  as  before.  In  all  these  readings  care  should  be  taken  that  the 
needle  moves  freely  upon  its  axis  and  does  not  come  to  rest  too  soon. 
Make  a  record,  as  shown  in  the  table,  and  take  an  average  of  the 

readings.    The  average  is  the  angle 
of  dip  for  the  locality. 

EXPERIMENT  20. — To  determine 
the  angle  of  dip  in  vertical  planes 
not  in  the  magnetic  meridian. 

Apparatus.  —  The  dipping  needle 
used  in  the  last  experiment. 

Manipulation.  —  Turn  the  stand- 
ard of  the  instrument  through 
90  degrees,  taking  a  reading  of 
the  needle  every  five  degrees,  and 
make  a  table  of  the  results. 


POSITION 

END  OF  NEEDLE 

RKADIXG 

No.  1 

{  Upper    .     . 
1.  Lower    .     . 

— 

No.  2 

j  Upper    .     . 
!  Lower    .     . 

— 

No.  3 

/Upper    .     .' 
[  Lower    .     . 

/ 

No.  4 

/Upper    .... 
[  Lower    .     . 

— 

Average, 

— 

22 


MAGNETISM 


Make  a  curve  having  for  the  horizontal  axis  the  angle  through 
which  the  standard  is  turned,  and  for  the  vertical  axis  the  reading 
of  the  dipping  needle. 

20.   The  Graphical  Method  of  Recording  an  Experiment.  — 

One   of  the   most   satisfactory  methods  of  recording  the 


AMJI.K 

DIP 

CHANGE 

ANGLE 

DIP 

CHANGE 

AN<;L  i: 

DIP 

CHANGE 

0 

71.50 

35 

75.75 

1.00 

70 

84.00 

1.25 

5 

71.75 

.25 

40 

76.75 

1.00 

75 

85.50 

1.25 

10 

72.00 

.25 

45 

77.75 

1.00 

80 

87.00 

1.50 

15 

72.75 

.75 

50 

79.00 

1.25 

85 

88.75 

1.75 

20 

73  50 

.75 

55 

80.00 

1.00 

90 

90.00 

1.25 

26 

74.00 

.50 

CO 

81.50 

1.50 

:JO 

74.75 

.75 

65 

82.75 

1.25 

70 


10 


30°  40°  50°  60° 

DECLINATION  FROM  THE  MERIDIAN 

FIG.  17 


70 


80" 


results  of  an  experiment  is  the  graphical  method,  or  curve. 
This  is  made  by  laying  off  on  cross-section  paper  one  set 
of  conditions  in  one  direction,  and  at  a  right  angle  to  it 
the  results  that  are  to  be  compared  with  them.  Two 
lines  are  usually  selected  as  axes,  the  horizontal  being 


THE  GRAPHICAL  METHOD 


23 


called  the  axis  of  X  and  the  vertical  the  axis  of  Y. 
Figure  17  gives  the  curve  for  Experiment  20.  An  inspec- 
tion of  this  curve,  and  a  comparison  of  it  with  the  table 
from  which  it  was  formed,  will  show  how  it  was  drawn. 
One  advantage  of  this  form  of  record  is  that  points  not 
determined  by  the  experiment  are  interpolated  by  the 
curve. 

21.  Application  of  the  Dipping  Needle  to  Finding  the 
Poles  of  a  Bar  Magnet.  —  Since  the  direction  of  a  short 
dipping  needle  at  any  point  is  parallel  to  the  direction  of 
the  magnetic  lines  of  force  at  that  point,  it  is  possible  to 
locate  the  poles  of  a  bar  magnet  as  follows : 

EXPERIMENT  21.  —  To  locate  the  poles  of  a  bar  magnet. 
Apparatus.  —  A  dipping  needle,  supported  as  shown  in  Fig.  18,  and 
a  long  bar  magnet. 


FIG.  18 


Manipulation.  —  Draw  a  line  across  the  middle  of  the  magnet  and 
call  it  zero.  Draw  similar  lines  across  the  magnet  at  intervals  of 
a  centimeter,  numbering  them  from  the  middle  toward  each  end. 

Lay  the  magnet  upon  a  table  in  the  magnetic  meridian  and  place 
the  base  of  the  dipping-needle  stand  —  which  should  be  an  even  num- 
ber of  centimeters  in  length  —  in  such  a  position  that  the  axis  of  the 
needle  is  vertically  above  the  middle  of  the  magnet. 

Move  the  magnet  lengthwise  one  centimeter  at  a  time,  and  take  a 
reading  of  both  ends  of  the  needle  for  each  position.  Tabulate  the 
results,  and  from  the  table  thus  formed  construct  a  curve  that  shall 
have  the  distance  of  the  middle  of  the  needle  from  the  middle  of  the 
magnet  laid  off  along  the  axis  of  X,  and  the  angle  of  dip  laid  off  along 
the  axis  of  Y. 


24  MAGNETISM 

The  location  of  the  poles  will  be  indicated  by  those  points  of  the 
curve  that  correspond  to  a  dip  of  90  degrees. 

It  will  be  observed  that  the  position  which  the  dipping  needle 
takes  is  in  every  case  due  to  the  resultant  of  the  magnetic  forces  of 
both  the  earth  and  the  magnet  under  consideration.  A  curve  made 
from  the  average  of  two  sets  of  readings,  one  taken  when  the  bar 
magnet  lies  with  its  N  pole  to  the  magnetic  north,  and  one  when 
it  lies  with  its  S  pole  to  the  magnetic  north,  will  give  the  most 
accurate  result. 

22.  Magnetic  Declination.  —  Observation 
shows  that  in  most  places  the  magnetic 
meridian  and  the  geographical  meridian  do 
not  coincide.  In  the  eastern  part  of  the 
United  States  the  needle  points  to  the  west, 
and  in  the  western  part  to  the  east,  of  the 
true  north.  The  angle  which  measures  the 
difference  is  called  the  declination.  It 
changes  slowly  from  year  to  year,  and  is  also 
subject  to  a  slight  daily  change  and  to  acci- 
dental changes.  These  are  called  variations 
FIG.  19  in  the  declination. 

23.  Measurement  of  the  Decimation.  —  The  method  of 
determining  the  declination  is  generally  that  of  determin- 
ing the  true  north  by  reference  to  the  position  of  the 
North  Star.  If  this  star,  Polaris,  were  at  the  exact  north 
pole  of  the  heavens,  it  would  give  the  direction  of  the 
true  meridian  at  all  times ;  but  as  it  is  nearly  one  and  one 
quarter  degrees  away,  it  is  on  the  meridian  only  twice  in 
twenty-four  hours,  when  it  is  directly  above  and  when 
it  is  directly  below  the  pole,  as  in  Fig.  20  at  A  and  C. 
At  points  midway  between  these,  as  at  B  and  Z>,  it  is  at 
its  greatest  elongation  either  east  or  west. 

The  full  line  in  Fig.  20  represents  a  photograph  made 


MAGNETIC  DECLINATION 


25 


by  exposing  a  plate  in  a  camera  for  nearly  twelve  hours, 
and  letting  the  trail  of  Polaris  fall  upon  it.  The  dotted 
line  gives  its  path  for  the  remaining  hours  of  the  day. 
In  order  to  give  an  idea  of  the  distance  of  Polaris  from 
the  north  pole,  a  representation  of  the  moon  on  the  same 
scale  is  placed  here  for  comparison. 


MOON  ON 
SAME  SCALE 


FIG.  20 

EXPERIMENT  22. —  To  measure  the  magnetic  declination. 

Apparatus.  —  A  surveyor's  compass  or  transit. 

Manipulation.  —  Set  up  and  level  the  transit  in  a  room  in  such  a 
position  that  the  North  Star  can  be  seen  through  an  open  window. 
Choose  such  a  time  of  night  that  the  constellation  of  the  Great  Bear 
is  either  east  or  west  of  Polaris.  Bring  the  vertical  cross  hair  of  the 
instrument  to  cover  the  star,  and  watch  it  until  it  seems  to  stand  still, 
moving  neither  to  the  right  nor  to  the  left.  When  this  position  is 
found,  it  is  in  position  either  B  or  D  (Fig.  20).  Release  the  compass 
needle  on  the  transit  and  let  it  come  to  rest.  Read  the  position  of 
the  needle;  this  reading,  corrected  for  the  angular  distance  of  Polaris 
from  the  North  Pole,  will  be  the  declination. 

By  leaving  the  transit  undisturbed  in  its  position  until  morning, 
both  the  geographic  and  the  magnetic  meridian  can  be  laid  out  per- 
manently. 


26 


MAGNETISM 


To  find  the  True  Meridian.  —  Make  the  correction  for  the  angular 
distance  of  Polaris,  and  place  a  mark  in  the  floor  vertically  under  the 
instrument.    Place  another  on  a  stone  set  in  the  ground  at  a  distance  of 
a  hundred  yards,  and  in  the  line  determined  by  the  vertical  cross  hair. 
0  To   determine   the    Magnetic    Meridian.  — 

Bring  "the   needle   to  read   zero,   and   then 
determine  a  mark  in  a  second  stone. 

NOTE.  —  If  the  Great  Bear  does  not  come 
to  the  east  or  west  of  .Polaris  at  a  convenient 
hour,  the  reading  can  be  taken  when  it  is  in 
the  position  shown  in  Fig.  21. 

The  north  pole  is  in  the  meridian  of 
Polaris  when  the  vertical  cross  hair  passes 
through  both  Polaris  and  the  second  star  in 
the  handle  of  the  Dipper  as  shown. 


X 


FIG.  21 


The  angular  distance  of  Polaris 
from  the  north  pole  is  diminishing 
at  the  rate  of  about  twenty  seconds 
of  arc  per  year.  In  1900  its  distance 
was  1°  13'  32".  In  1915  it  will  be  1°  8'  53".  The  fol- 
lowing table  gives  the  times  of  greatest  elongation  for  the 
first  day  of  each  month  of  the  year : 

MAXIMUM  ELONGATIONS  OF  POLARIS 


MONTH 

EASTERN 

WESTERN 

MONTH 

EASTERN 

WESTERN 

Jan. 

0.27  P.M. 

0.19  A.M. 

July 

0.35  A.M. 

0.23  P.M. 

Feb. 

10.24  A.M. 

10.  13  P.M. 

Aug. 

10.30  P.M. 

10.22  A.M. 

Mar. 

8.34  A.M. 

8.22  P.M. 

Sept. 

8.28  P.M. 

8.20  A.M. 

Apr. 

6.32  A.M. 

6.20  P.M. 

Oct. 

6.30  P.M. 

6.22  A.M. 

May 

4.34  A.M. 

4.22  P.M. 

Nov. 

4.28  P.M. 

4.21  A.M. 

June 

2.33  A.M. 

2.21  P.M. 

Dec. 

2.30  P.M. 

2.22  A.M. 

It  will  be  observed  that  at  times  approximately  six  hours 
earlier  or  six  hours  later  than  those  given  above  Polaris 
will  be  in  the  position  represented  by  Fig.  21,  or  by  that 
figure  inverted. 


DISTRIBUTION   OF  MAGNETISM  27 

24.  Distribution  of  Magnetism  along  a  Bar  Magnet. — 

One  of  the  methods  employed  for  measuring  the  magnetic 
intensity  at  any  point  is  that  of  vibrating  a  magnetic 
needle  at  that  point,  and  is  called  the  method  of  vibrations. 
Whenever  a  magnetic  needle  is  deflected  from  its  position 
of  rest,  it  will  set  up  a  series  of  vibrations  which,  like 
those  of  a  pendulum,  are  made  in  equal  times. 

The  intensity  of  any  magnetic  field  is  directly  propor- 
tional to  the  square  of  the  number  of  vibrations  per  minute 
of  a  magnetic  needle  suspended  in  that  field.  If  a  needle 
vibrates  N times  per  minute  when  acted  upon  by  both  a  bar 
magnet  and  the  earth,  and  n  times  when  acted  upon  by 
the  earth  alone,  then  the  intensity  of  the  magnetic  field  due 
.to  the  magnet  alone  will  be  proportional  to  N2  —  n2  at  that 
point. 

EXPERIMENT  23. —  To  determine  the  distribution  of  magnetism 
along  a  bar  magnet. 

Apparatus.  —  Two  bar  magnets ;  a  magnetic  needle  suspended  so  as 
to  be  free  from  air  currents  (an  Erlenmeyer  flask  will  answer)  ;  and  a 
support  for  the  magnet.  In- 
crease the  weight  of  the 
needle  by  splitting  a  lead 
ball  and  pinching  it  on  as  in 
a,  Fig.  22. 

Manipulation.  —  Place  the 
support  for  the  magnet  — 
which  must  be  made  without 
using  either  iron  or  steel  — 
so  that  a  line  drawn  across 
the  middle  of  the  £op  will  be 
in  the  magnetic  meridian. 
Place  the  flask  containing  the  _, 

needle  upon  the  line  and  make 

sure  that  there  is  no  twist  in  the  suspension ;  the  needle  will  then  come 
to  rest  directly  over  the  line. 

Deflect  the  needle  by  bringing  bar  magnet  No.  1  toward  the  flask 


MAGNETISM 


POSITION 

OF 

NEEDLE 

NUMBER 

OF 

VIBRATIONS 

COMPARATIVE 
INTENSITIES 

Earth  alone 

71  =  5 

n2  =  25 

End  of  mag. 
1st  mark 

2V  =23 

N=25 

/V2-w2  =  504 
N2-n2  =  600 

2d  mark 

N=22 

Ni-ri2  =  45Q 

Figure 


from  either  the  east  or  the  west.  Be  careful  that  the  needle  does  not 
swing  as  a  pendulum.  Determine  the  time  it  takes  for  50  vibrations  and 
compute  the  number  per  minute.  Draw  lines  across  bar  magnet  No.  2 
at  intervals  of  a  half  inch,  beginning  at  each  end,  and  fasten  the  mag- 
net on  the  side  of  the  box,  as  shown  in  the  figure,  so  that  the  needle 
will  be  on  a  level  with  the  end.  Put  the  needle  in  vibration  as  before 
and  determine  the  number  of  vibrations  per  minute.  Do  this  for 
every  half  inch  of  the  magnet  until  the  middle  is  reached.  Turn 
the  box  around,  reverse 
the  magnet,  and  make  the 
same  experiments  for  the 
other  half. 

Arrange  the  results  as 
in  the  table,  and  make  a 
graphical  record  of  the 


23  shows  how  the  graphical  record  is  made.  First  a 
drawing  is  made  of  the  bar  magnet,  then  from 
the  end  and  from  each  half-inch  mark  distances 
&'  aa',  W,  etc.,  are  laid  off  to  scale,  representing  the 
values  of  JV2  —  ri2  at  the  different  positions  on 
the  magnet.  By  connecting  the  points  a',  &',  c', 
etc.,  by  a  curved  line,  the  figure  will  be  made  to 
represent  the  distribution  of  magnetic  force  along 
the  magnet. 

By  continuing  the  curve  for  the  whole  length 
of  the  needle,  the  position  of  each  pole  is  shown 
to  be  at  some  distance  from  the  end,  and  the 
question  whether  the  magnetism  is  symmetrically 
distributed  or  not  is  determined. 

The  above  table  and  the  curve  of  distribution 
FIG.  23  are  from  a  part  of  the  results  of  an  experiment. 


25.  Action  of  a  Magnet  upon  a  Needle.  —  It  was  shown 
in  Section  17  that  the  expression  for  the  terrestrial  mag- 
netic couple  that  tends  to  bring  the  needle  back  into  the 
meridian  whenever  it  is  deflected,  is  MH  sin  a,  in  which 
M  is  the  magnetic  moment  of  the  needle,  or  the  product 


ACTION   OF  A   MAGNET   UPON  A   NEEDLE 


29 


of  the  strength  of  one  of  its  poles  by  the  distance  between 
them,  H  is  the  horizontal  component  of  the  earth's  mag- 
netism, and  a  is  the  angle  of  the  deflection.  Suppose  a 
magnet  NS  to  be  placed  in  an  east-and-west  line  near  a 
magnetic  needle  us,  as  in  Fig.  24,  and  to 
keep  it  deflected  from  the  magnetic  meridian 
at  the  angle  a.  Let  the  strength  of  each  pole 
of  the  magnet  be  w,  and  of  the  needle  m1 . 
Let  the  length  of  the  magnet  be  2  Z,  of  the 
needle  2  Z,  and  let  the  distance  between  their 


—  2L- 


I 


FIG.  24 


centers  be  d.     Since  I  is  small  compared  with 
d,  the  force  acting  between  S  and  n  will  be 

-,  and  the  force  acting  between  N 


and  n  will  be  H — 


mm 


mm 


mm 


(<* 

i 


;,  while  the  total  force  will  be 

4  mm1 Ld  rrn         £  A.' 

The  force  acting 


(<*  +  £)'      (<*>-£)»,        (#; 

upon  s  will  be  H — !^m      g-    Since  this  force  acts  at  nearly 

a  right  angle  to  the  needle,  the  moment  of  the  couple 
acting  at  n  and  s  may  be  taken  as 

4  mm'Ld  ,-,  7  8  mm'Itdl  cos  a 

2  I  cos  a  = 


As  this  is  the  moment  of  the  deflecting  force  which 
keeps  the  needle  in  equilibrium,  it  must  be  equal  to  the 
moment  of  the  magnetic  couple  of  the  earth ;  hence. 


30  MAGNETISM 


(d2  -  L2)2 
8  mm'Ldl  cos  a 

(rf2- 


or  2  m'lffs'm  a  = 


£  i  •    i  XT-    •  4  7ft^>C?  COS  a  ixi- 

from  which  we  get  //sin  a  =  —  —  -  ^yT'  a  reduces 


to  =        "^          tan  a.     Since    2mL  =  M,   the   mag- 

JZ  ^  6& 

iietic  moment  of  ^ZViS,  the  equation  becomes 


If  d  is  great  as  compared  with  L,  the  equation  reduces,  as 

M     d3 
an  approximation,  to  —  =    -tana,   an  expression  which 

-TZ  — 

gives  the  ratio  of  the  magnetic  moment  of  a  given  magnet 
to  the  horizontal  component  of  the  earth's  magnetism,  in 
terms  of  the  distance  between  the  centers  of  the  magnet 
and  of  the  magnetic  needle,  and  the  tangent  of  the  angle 
of  deflection  produced. 

This  position  of  the  magnet  with  relation  to  the  needle, 
shown  in  Fig.  24,  is  called  the  "A  tangent  position  of 
Gauss."  In  the  "B  tangent  position"  the  magnet  is 
placed  parallel  to  the  needle. 

P^XPERIMENT  24.  —  To  investigate  the  A  tangent  position. 

Apparatus.  —  A  small  bar  magnet  ;  meter  scale  ;  and  a  deflection 
magnetometer  or  compass. 

Manipulation.  —  Place  the  magnetometer  in  such  a  position  that 
the  needle  will  read  zero  when  it  conies  to  rest.  Cut  a  short  piece 
from  the  meter  stick  and  fix  the  stick  upon  a  support  in  an  east-and- 
west  line  opposite  the  middle  of  the  needle  in  such  a  position  that  the 
distances  are  laid  off  from  that  point.  Place  the  bar  magnet  on  the 
scale  with  its  middle  at  the  distance  of  one  meter  from  the  middle  of 
the  needle  and  read  the  deflection.  Move  the  magnet  along  the  scale 


THE   VIBRATION  OF  A   MAGNET 


31 


toward  the  needle  and  take  a  reading  of  the  deflection  at  every  centi- 
meter. Plot  a  curve  from  the  results  obtained,  laying  off  distances 
along  the  axis  of  X  and  deflections  along  the  axis  of  Y. 

A  study  of  the  curve  obtained  will  show  the  change  in  the  deflec- 
tion that  takes  place  as  the  magnet  is  brought  near  the  needle,  and 
the  varying  rate  of  the  change. 

A  reflecting  galvanometer  with  a  short  needle  makes  a  good  mag- 
netometer for  this  experiment. 


FIG.  25 

Let  AB  represent  the  meter  scale,  fastened  to  a  board  with  a 
groove  in  it,  in  which  the  magnet  NS  can  slide.  When  the  deflection 
of  the  needle  is  the  angle  OMC,  the  reading  is  for  the  angle  OMD. 
If  the  distance  OM  is  taken  as  unity,  the  reading  of  the  scale  OD 
will  be  the  tangent  of  twice  the  angle  of  deflection.  If  the  distance 
OM  be  one  half  a  meter,  the  millimeter  divisions  on  the  scale  OD 
will,  for  small  deflections,  be  nearly  the  natural  tangent  of  the  angle 
of  deflection. 


26.  The  Vibration  of  a  Magnet.  — A  suspended  magnet, 
or  magnetic  needle,  vibrates  with  a  simple  harmonic 
motion  like  a  pendulum.  The  time  of  its  vibration  is 

given  by  the  expression  t  =  TT^/ ,  in  which  I  is  the 

moment  of  inertia  of  the  magnet,  Mits  magnetic  moment, 
and  H  the  horizontal  component  of  the  earth's  magnetism. 


32 


MAGNETISM 


The  moment  of  inertia  can  be  calculated  by  the  following 
rules  : 

(a)  For  a  cylindrical  magnet  supported  as  in  Fig.  26, 


—  1- 


FIG.  26 


In  this  expression  W  is  the  mass, 
I  the  length,  and  r  the  radius  of  the 
magnet. 

(5)  For  a  bar  magnet  of  rectangu- 
lar cross  section,  suspended  as  in 


Fig.  27,  1=  W 


12   / 

and  b  are  the  dimensions  of  the  horizontal  sides. 
From  the  expression  for  the  time  of  a  vibration, 


we  get     t2  = 


in  which  I 


MJf 


hence  MH= 


7T2/ 

Ml? 

7T2/ 
t*    ' 


EXPERIMENT  25.  —  To  determine  the  value  of  MH  for  a  given 
magnet. 

Apparatus.  —  A  short  bar  magnet  and  vibration  box,  as  shown  in 

Fig.  28 ;  and  a  brass  bar  of  the 
same  weight  as  the  magnet. 

Manipulation.  —  Set    the    box 
so  that  its  sides  shall  be  in  the 
magnetic  meridian.      Place  the 
JV    brass    bar    in    the    stirrup    and 


twist  the  suspension  head  until 
the  bar  is  directly  over  the  line 
Remove  the  brass  bar  and 


FIG.  28 

NS,  drawn  on  the  bottom  of  the  box. 
substitute  the  magnet  for  it.  Put  the  magnet  in  vibration  by  bringing 
the  end  of  another  magnet  up  to  the  side.  Determine  the  time  of 
vibration.  Repeat  and  take  the-  average. 


THE  VIBRATION  OF  A   MAGNET  33 

By  determining  the  time  for  several  sets  of  vibrations  the  fact  that 
they  are  isochronous  will  be  observed.  By  computing  the  value  of  7 
by  one  of  the  rules  given  above,  and  substituting  this  value  and  the 
value  of  t  determined  in  the  experiment,  the  value  of  the  product  MH 
is  determined. 

27.    The  Determination  of  M  and  //.  —  From  the   two 
formulas,  Mff=^~,  and  ^=  (^ ~^2)2 tan  a,  we  obtain 
values  for  M  and  H  as  follows  : 
From  the  first      M  = 


From  the  second  M  =  ±^-   ~-±£L  tan  a. 

2  d 

Equating  these  values  of  M  and  reducing,  we  get 

=  ___^ 

X     1O  T"ON 

and  in  a  similar  way  M  - 

By  substituting  in  these  formulas  the  results  obtained 
in  Experiments  24  and  25,  the  values  of  M  and  H  are 
obtained. 

28.    To  compare  the  Magnetic  Moments  of  Two  Magnets. 
-  It  is  sometimes  necessary  to  determine  the  comparative 
values  of  the  moments  of  magnets.     This  may  be  done 
as  follows : 

EXPERIMENT  26.  —  To  compare  the  values  of  M  in  magnets. 

Apparatus.  —  The  magnetometer  used  in  Experiment  24 ;  a  stand- 
ard magnet ;  and  magnets  to  be  compared. 

Manipulation.  —  Place  the  standard  magnet  —  which  should  be  a 
short  magnet  highly  magnetized  —  at  such  a  distance  from  the  needle, 
say  500  cm.,  that  it  will  give  a  convenient  deflection.  Place  one 

ELEC.   AND  MAG.  3 


34  MAGNETISM 

of  the  other  magnets  on  the  opposite  side  of  the  magnetometer  at 
such  a  distance  that  the  deflection  is  brought  back  to  zero. 

Let  M  be  the  moment  of  the  standard  magnet  and  d  the  distance  of 

its  center  from  the  needle;  then,  from  Section  25,  —  =  —  tana.     In 

71  jy         x7/3  "^  w 

the  same  way  - —  =  —  tan  a,  in  which  M  and  d'  are  corresponding 

H       2 
values  for  the  second  magnet.     Combining  these  expressions,  we  get 

—  =  — ;  that  is,  the  magnetic  moments  of  the  magnets  are  directly 

Mf     d'B 

proportional  to  the  cubes  of  the  distances  that  give  a  zero  deflection. 

PRACTICAL  QUESTIONS  AND  PROBLEMS 

1.  Suppose  that  in  some  way  the  polarity  of  a  magnetic  needle  has 
become  reversed.     With  which  pole  of  a  magnet  will  you  stroke  the 
original  north  pole  of  the  needle  to  restore  it  to  its  proper  condition  ? 

2.  Can  you  devise  a  form  of  experiment  in  which  the  change  of 
the  magnetic  moment  of  a  magnet  due  to  a  change  of  temperature 
can  be  shown  and  measured? 

3.  What  is  the  value  of  the  horizontal  component  of  the  earth's 
magnetism  at  a  place  where  the  dip  is  71°  27'  and  the  intensity  is  .605  ? 

4.  Why  does  the  dipping  needle  stand  in  a  vertical  direction  when 
its  axis  is  in  the  plane  of  the  magnetic  meridian  ? 

5.  The  blade  of  a  steel  table  knife  can  be  magnetized  by  laying 
it  on  a  table  and  stroking  it  with  one  end  of  a  fire  poker  held  in  a 
vertical  direction.     Why  ? 

6.  In  1861  a  survey  was  made  of  a  quarter  section  — 160  acres  —  of 
land  having  the  first  line  in  the  magnetic  meridian.      Show  by  a 
drawing  the  error  that  would  be  made  by  surveying  the  land  accord- 
ing to  the  old  minutes,  in  1900,  if  the  average  annual  increase  in  the 
western  declination  has  been  7'. 

7.  A  magnetic  needle  vibrated  6  times  per  minute  in  the  place 
mentioned  in  Problem  3.    'What  is  the  intensity  of  the  field  of  a  bar 
magnet,  if  the  same  needle  vibrates  29  times  per  minute,  due  to  both 
the  earth  and  the  magnet  acting  together  ? 

8.  A  certain  magnet  vibrates  32.2  times  per  minute  in  New  York 
and  36  times  in  Philadelphia.     What  are  the  relative  values  of  H  in 
the  two  places  ? 


CHAPTER    II 
ELECTRICITY 

29.  The  Electric  Current.  —  Whenever  the  ends  of  a  wire 
are  connected  to  the  poles  of  a  voltaic  cell  or  battery,  phe- 
nomena take  place  in  and  around  the  wire  that  are  the 
effects  of  what  is  called  an  electric  current  in  the  wire. 
These  effects  may  be  grouped  in  three  classes  and  are 

called:  i  4    rpi  ±-      cc 

1st.    I  he  magnetic  etiect; 

2d.    The  chemical  effect; 
3d.    The  heating  effect. 

It  is  worthy  of  notice  that  identical  electric  currents 
can  be  obtained  in  three  ways,  and  that  these  currents 
are : 

1st.  The  currents  derived  from  an  electrical  conductor 
cutting  lines  of  magnetic  force  ; 

2d.    The  currents  derived  from  chemical  action  ; 
3d.    The  currents  derived  from  the  action  of  heat. 

The  experiments  that  follow  are  designed  to  make  the 
student  familiar  with  the  different  effects  of  electric  cur- 
rents, and  to  give  some  facility  in  the  measurements  of 
these  effects. 

30.  Magnetic  Effects  of  the  Current  —  EXPERIMENT  27.— 

Oersted's  experiment. 

Apparatus.  —  Any  form  of  galvanic  cell ;  a  piece  of  insulated  cop- 
per wire  three  feet  long  or  more ;  a  magnetic  needle. 

35 


36  ELECTRICITY 

Manipulation.  —  Connect  the  ends  of  the  wire  to  the  terminals  of 
the  cell.  Hold  the  wire  above,  and  parallel  to,  the  magnetic  needle. 
Observe  the  action  of  the  current  upon  the  needle.  Reverse  the  direc- 
tion of  the  current  and  observe.  Place  the  wire  below  the  needle. 
Repeat  both  experiments.  Formulate  a  law  that  shall  express  the 
relation  between  the  direction  of  the  current  and  the  direction  of 
deflection  of  the  north  end  of  the  needle.  Assume  that  the  current 
flows  in  the  external  circuit  from  the  copper  or  carbon  terminal  to 
the  zinc  terminal.  This  makes  the  copper  terminal  the  +  pole,  and 
the  zinc  terminal  the  —  pole. 

This  experiment  was  first  made  by  Oersted,  a  Danish 
physicist,  in  1820,  and.  established  the  relation  between 
electricity  and  magnetism.  Ampere,  who  studied  the 
experiment  carefully,  stated  the  law  of  deflection  as  fol- 
lows :  If  one  considers  himself  a  swimmer  going  along 
the  wire  in  the  same  direction  as  the  current  and  always 
facing  the  needle,  the  north  end  of  the  needle  will  be 
deflected  toward  the  swimmer's  left  hand. 

A  convenient  statement  of  the  law  is :  Let  the  fingers 
of  the  right  hand  point  in  the  direction  in  which  the  cur- 
rent is  going,  with  the  palm  always  turned  toward  the 
needle ;  then  the  north  pole  of  the  needle  will  be  deflected 
toward  the  thumb. 

This  law  is  fundamental  and  should  be  made  very 
familiar. 

EXPERIMENT  28.  —  An  extension  of  Experiment  27. 

Apparatus.  —  A  magnetic  needle ;  a  flat  coil  of  wire  long  enough  to 
inclose  the  needle;  two  cells  of  a  battery;  and  a  switch. 

Manipulation.  —  Place  the  needle  inside  the  coil,  turning  the  coil 
until  it  is  parallel  to  the  needle  when  it  comes  to  rest.  Couple  the 
terminals  of  one  cell  to  the  coil,  close  the  switch,  and  observe  the 
deflection.  Compare  it  with  the  deflection  obtained  in  Experiment  27. 
Couple  both  the  cells  in  series  with  the  coil  and  observe  the  deflection.. 
Compare  it  with  the  deflection  when  one  cell  was  used. 


MAGNETIC  EFFECTS   OF  THE  CURRENT  37 

Cells  are  coupled  in  series  when  the  copper  terminal  of  one  is 
coupled  to  the  zinc  terminal  of  the  other,  as  in  Fig.  29. 

CELLS  IN  SERIES  , 
—  I        I     + 


Cu 


X, 


\SS  EXTERNAL  CIRCUIT 

FIG.  29 


They  are  coupled  in  parallel  when  the  copper  terminals  are  coupled 
together,  and  the  zinc  terminals  are  coupled  together,  as  in  Fig.  30. 
This   experiment    shows 


CELLS  IN  PARALLEL 

that  a  coil  of  wire  carrying 


a  current  deflects  a  magnetic    GoQQQOOQ 


needle    through    a    greater        EXTERNAL  C.RCU.T 

angle    than    a    single   wire 

does,  and  that  two  cells  produce  a  greater  effect  than  one. 

One  class  of  galvanometers,  called  galvanometers  of  the  first  class, 
makes  use  of  the  principle  brought  out  in  this  experiment. 

EXPERIMENT  29.  —  -  An  examination  of  deflection  galvanometers. 

Apparatus.  —  A  cell;  connecting  wires;  several  galvanometers  of 
the  first  class. 

Manipulation.  —  Couple  each  galvanometer  to  the  cell  in  turn  and 
determine  the  direction  of  the  deflection.  From  the  observed  deflec- 
tion determine  the  direction  of  winding  in  each  galvanometer. 

Make  a  list  of  the  galvanometers  examined,  and  state  why  they 
are  of  the  first  class. 

EXPERIMENT  30.  —  The  principle  of  the  solenoid  galvanometer. 
Apparatus.  —  The  coil,  iron  core,  and  balance  shown  in  Fig.  31;  a 
number  of  cells  ;  and  a  switch. 


88 


ELECTRICITY 


Manipulation.  —  Suspend  the  iron  core  from  one  scale  pan  of  the 
balance  so  that  its  upper  end  shall  be  2  in.  or  3  in.  above  the  top  of 

the  coil.  Couple  a 
cell  to  the  coil,  having 
a  switch  in  the  cir- 
cuit. Close  the  switch 
and  send  the  current 
through  the  coil. 
Observe  any  change 
that  takes  place  in 
the  position  of  the 
iron  core.  Find  the 
weight  necessary  to 
bring  the  beam  back 
to  a  horizontal  posi- 
tion. Couple  two 
cells  in  series  and  re- 
peat the  experiment. 

This  experiment 
shows  that  an  elec- 
tric current  passing 
through  a  coil  of  wire 
tends  to  draw  an  iron 


core  to  its  center. 

FlG  31  This   is  the   prin- 

ciple   upon    which    a 

second  class  of  galvanometers  operate.     They  are  called  solenoid  gal- 
vanometers. 

EXPERIMENT  31. — The  effect  of  a  current  in  a  coil  upon  an  iron  core. 

Apparatus.  —  Cells;    insulated  wire;    switch;   soft  iron  rod;   and 
iron  filings. 

Manipulation.  —  Wind  the 
wire  closely  around  the  iron 
rod  and  couple  it  to  one  of 
the  cells,  putting  the  switch  in 
the  circuit,  as  in  Fig.  32.  Dip 
the  end  of  the  iron  rod  in  the 
iron  filings  to  test  it  for  mag- 
netism when  the  switch  is  open.  Close  the  switch,  sending  the  cur- 


MAGNETIC  EFFECTS   OF  THE  CURRENT  39 

rent  through  the  coil,  and  again  test  the  rod  for  magnetism.  Repeat 
with  all  the  cells  in  series. 

The  results  of  this  experiment  show  that  whenever  a  current  of 
electricity  passes  through  a  coil  of  wire  wound  around  an  iron  rod, 
the  rod  becomes  magnetized,  and  that  the  strength  of  its  magnetism 
increases  with  the  strength  of  the  current. 

NOTE.  —  In  all  experiments  in  which  the  electric  current  is  used, 
care  should  be  taken  that  all  contacts,  at  the  binding  posts  and  other 
couplings,  are  well  made,  since  a  poor  contact  either  weakens  the 
current  or  makes  it  unsteady.  The  current  should  be  cut  off  by  the 
switch  as  soon  as  the  experiment  is  finished,  since  the  current  from 
many  forms  of  cells  grows  weaker  the  longer  they  are  used  continu- 
ously. The  student  must  not  expect  that  the  current  from  a  battery 
will  go  from  one  point  to  another  unless  a  conducting  path  is  fur- 
nished. This  path  is  usually  a  metallic  conductor,  such  as  a  wire, 
and  the  student  can  form  no  better  habit  than  that  of  tracing  out  the 
path  of  the  current  in  every  connection  that  he  makes. 

EXPERIMENT  32.  —  To  determine  the  relation  between  the  direc- 
tion of  the  current  in  a  coil  and  the  polarity  of  its  core. 

Apparatus.  —  The  cells,  coil,  iron  core,  and  switch  used  in  Experi- 
ment 31 ;  and  a  magnetic  needle. 

Manipulation.  —  Couple  the  apparatus  as  in  the  preceding  experi- 
ment and  send  the  current  through  the  coil.  Determine  the  polarity 
of  the  core  by  bringing  each  end  alternately  near  the  poles  of  the 
needle.  Reverse  the  current  in  the  coil  and  repeat. 

Formulate  a  law  showing  the  relation  between  the  direction  of 
the  current  in  the  coil  and  the  resulting  polarity  of  the  core. 

One  statement  of  the 
law  is  as  follows:  If  the 
coil  is  grasped  in  the  right 
hand  in  such  a  manner  that 
the  fingers  point  in  the 
same  direction  as  that  in 
which  the  current  is  pass- 
ing, then  the  thumb  will 

point  to  the  north  pole  of  the  core,  as  in  Fig.  38.  Does 
the  experiment  verify  this  law  ? 


40  ELECTRICITY 

31.  Electro-magnets.  —  The  combination  of  coil  and  iron 
core  described  in  the  last  two  experiments  constitutes  an 
electro-magnet.     Electro-magnets  are  used  for  many  pur- 
poses, in  nearly  all  of  which  an  important  factor  is  the 
readiness  with  which  the  core  becomes  demagnetized  on 
breaking  the  current.      The   form  is  usually  that  of  a 
horseshoe  magnet  wound  in  such  a  way  that  one  of  the 
poles  shall  be  -ZVand  the  other  8.     The  armature  is  a  piece 
of  soft  iron  placed  directly 

in  front  of  the  poles.  As 
long  as  the  current  is  pass- 
ing through  the  coil,  the 
armature  is  held  against 
the  poles;  but  when  the  FlG  ^ 

circuit  is  broken  and  the 

current  is  consequently  stopped,  the  armature  is  moved 
away  by  a  spring,  as  shown  in  Fig.  34. 

32.  The  Telegraph.  —  The   essential   parts  of   a   tele- 
graphic circuit  are  the  main  battery  and  line,  the  send- 
ing key,   and  the  receiving  instrument.     The  receiving 
instrument   consists  of  a  high   resistance  electro-magnet 
called  a  relay,  and  a  local  circuit.     The  function  of  the 
relay  is  to  make  and  break  the  local  circuit,  which  con- 
sists of  the  local  battery  and  line  and  a  low  resistance 
electro-magnet  called  the  sounder. 

EXPERIMENT  33.  —  To  set  up  and  operate  a  telegraph  line. 

Apparatus.  —  Cells ;  relays  ;  keys  ;  sounders ;  and  wire  for  the  main 
and  local  circuits. 

Manipulation.  —  Set  up  the  instruments  as  shown  in  Fig.  35.  This 
figure  shows  the  instruments  necessary  for  one  station  only.  Study 
the  operation  of  the  relay  and  sounder  when  the  circuit  is  made  and 
broken  by  the  key.  In  actual  telegraphic  work  a  single  wire  only  is 
employed,  the  earth  being  used  as  one  branch  of  the  circuit. 


THE   TELEGRAPH;    THE  ELECTRIC  BELL 


41 


NOTE.  —  Since  this  is  a  well-known  and  important  method  of  com- 
munication, the  student  should  study  the  circuits  carefully  and  be  able 
to  explain  fully  the  function  of  each  part  of  the  apparatus. 

LOCAL  BATTERY 


MAIN  BATTERY 


'h 


FIG.  35 


LOCAL  CIRCUIT 


33.  The  Electric  Bell.  —  Another  familiar  use  to  which 
the  electro-magnet  is  put  is  in  the  electric  bell.  In  the 
telegraph,  the  circuit  is  made  and  'broken  at  the  will  of 
the  operator  by  the  use  of  the  key ;  but  in  the  electric 
bell  the  circuit  is  made  and  broken  automatically,  as  long 
as  the  button  is  pushed. 

EXPERIMENT  34.  —  To  set  up  and  operate  an  electric  bell. 

Apparatus.  —  A  cell ;  push  button ;  connecting  wires ;  and  an  elec- 
tric bell. 

Manipulation.  —  Couple  the  cell,  push  button,  and  bell  in  series, 
and  study  the  action  of  the  bell  on  closing  the  circuit  with  the  push 
button. 

Make  a  drawing  showing  the  path  of  the  current  in  the  circuit,  and 
write  a  detailed  description  of  the  automatic  action  of  the  bell. 

EXPERIMENT  35.  —  To  determine  whether  electric  bells  should  be 
coupled  in  series  or  in  parallel. 

Apparatus.  —  A  second  bell  and  push  button,  in  addition  to  the 
apparatus  used  in  Experiment  34. 

Manipulation.  —  (a)  Couple  the  two  push  buttons  in  such  a  way 
that  either  of  them  will  ring  bell  No.  1. 

(ft)  Couple  the  two  bells  in  series  and  test  them. 

(c)  Couple  them  in  parallel  and  test  again. 

Write  the  results  of  experiments  (a),  (5),  and  (c),  and  explain 
why  the  bells  will  ring  better  with  one  coupling  than  with  the  other. 


42 


ELECTRICITY 


34.    The  Polarized  Bell.  —  A  bell  having  a  bar  magnet 
for  its  armature  is  called  a  polarized  bell.     This  armature 

swings  on  a  pivot  at  the 
middle  and  at  this  point 
carries  a  rod  on  the  end 
of  which  is  the  bell 
hammer.  There  are  two 
bells,  as  in  Fig.  36,  which 
are  sounded  by  the  alter- 
nate blows  of  the  hammer 
caused  by  the  vibrations 
of  the  rocking  armature. 
The  bell  is  operated  by 
an  alternating  current, 
and  is  used  in  telephone 
calls  and  for  testing  the 
connections  of  electrical 
circuits. 

EXPERIMENT  36.  —  The 
principle  and  operation  of  the 
polarized  bell. 

Apparatus.  —  A  polarized 
bell;  magneto;  wires;  cells; 
and  the  key  shown  in  Fig.  37. 
This  key  consists  of  a  brass 
spring  wire  KG,  screwed  to  a 
block  of  wood  at  C,  and 
looped  into  a  handle  at  K. 
At  A  and  B  are  pins  con- 
nected to  the  opposite  poles  of  the  cells  D  and  E. 

Manipulation.  —  (a)  Vibrate  the  free  end  of  the  key,  touching  the 
pins  A  and  B  alternately. 

(b)  Rotate  the  magneto  after  coupling  the  bell  to  it. 
Show  on  a  drawing  the  path  of  the  current  in  (a)  when  the  key 
touches  A ,  and  when  it  touches  B. 


FIG.  36 


THE  POLAKIZED  BELL 


43 


The  results  of  the  first  part  of  the  experiment  (a)  show  that  the 
direction  of  the  current  determines  which  of  the  bells  is  struck.  Make 
a  drawing  of  the  bell  with  detailed  winding,  and  determine  from  its' 


BELL 


FIG.  37 

movement  the  N  end  of  the  armature.  Verify  this  determination 
with  a  magnetic  needle. 

The  second  experiment  (b)  differs  from  the  first  in  the  rapidity  of 
the  strokes  only. 

NOTE. — A  magneto  is  a  small  dynamo  having  permanent  magnets 
for  its  field  and  giving  an  alternating  current. 

EXPERIMENT  37. —  The  use  of  the  polarized  bell  in  tracing  connec- 
tions. 

Apparatus.  —  Insulated  wire  and  a  large  tube  of  some  insulating 
material. 


FIG. 


Manipulation.  —  Cut  a  dozen  wires,  each  a  meter  long,  and  run  them 
through  the  insulating  tube  as  in  Fig.  38.  Attach  a  label  to  each  end 
of  every  wire,  each  having  a  different  number,  and  by  the  use  of  the 


44 


ELECTRICITY 


magneto,  or  of  the  key  used  in  Experiment  36,  and  the  polarized  bell, 
determine  which  terminals  belong  to  the  same  wire. 

NOTE. —  This  kind  of  work  has  to  be  done  in  finding  the  terminals 
of  telephone  circuits.  The  experiment  can  be  made  more  interesting 
and  useful  if  different  kinds  of  wire  are  used  and  their  contacts 
changed  within  the  tube. 

35.  Magnetism  of  a  Flat  Coil.  —  EXPERIMENT  38.  — To  show 
the  magnetic  effect  in  a  coil  of  one  turn. 

Apparatus. — Large  brass  wire;  a  stand  —  shown  in  Fig.  39  —  made 
of  half-inch  board;  a  magnetic  needle;  cells;  and  a  switch. 

Manipulation. —  Bend  the  brass  wire  into  the  form  of  a  ring  6  in. 
in  diameter,  and  fasten  it  to  the  upright  part  of  the  stand  with 

__ staples.    Connect  the  ends  of  the  ring 

to  a  pair  of  binding  posts;  connect 
the  cells  and  switch  in  series  with  the 
ring  and  close  the  switch.  Bring  one 
end  of  the  magnetic  needle  in  front 
of  the  ring  at  its  middle  and  deter- 
mine the  relation  between  the  direc- 
tion of  the  current  in  the  ring  and 
the  polarity  of  its  axis.  Bring  the 
same  end  of  the  magnet  to  the  other 
side  of  the  ring,  i.e.  to  the  back  of 
the  upright  support,  and  again  observe  the  relation.  Repeat  with 
the  other  end  of  the  needle. 

This  experiment  may  be  considered  as  an  extension  of  Experiment 
31,  by  reducing  the  coil  used  in  that  experiment  to  a  single  turn,  and 
removing  the  iron  core.  The  law  for  the  relation  between  the  direc- 
tion of  the  current  and  the  resultant  polarity  holds  in  this  case.  It 
may  also  be  expressed  as  follows  :  The  north  pole  of  the  ring  is  facing 
the  observer  when  the  direction  of  the  current  is  counter-clockwise. 

36.  The  Lines  of  Force  around  a  Conductor.  —  If  the 

space  around  a  conductor  is  explored  with  iron  filings,  it 
will  be  found  to  be  a  magnetic  field. 

EXPERIMENT  39.  —  To  find  the  direction  of  the  lines  of  force 
around  a  conductor. 


FIG.  39 


THE  LINES   OF  FORCE  AROUND  A   CONDUCTOR      45 

Apparatus.  —  A  plate  of  glass  or  a  smooth  card  with  a  wire  running 
through  it  perpendicular  to  the  surface;  a  source  of  electricity  capa- 
ble of  giving  a  current  of  twenty  amperes;  iron  filings;  and  a  sieve. 
Manipulation.  —  Couple  the  wire  to  the  source  of  current,  and  while 
the  current  is  passing  sift  the  filings  upon  the  plate.  Tap  the  plate 
lightly  with  a  pencil  and  observe  the  direc- 
tion of  the  lines  of  force. 

The  experiment  shows  that  the  lines  of 
force  are  circles  having  the  wire  as  a  center. 
By  placing  a  small  compass  on  the  plate 
near  the  wire  the  direction  of  the  lines  will 
be  shown  to  be  as  in  Fig.  40. 

This  experiment  is  satisfactory  with  a 
small  current  if  its  effect  upon  a  small 
magnetic  needle  alone  is  wanted,  but  in  order 
to  show  the  circular  character  of  the  lines  of 
force  by  the  use  of  iron  filings  a  heavy  cur- 
rent must  be  used. 

The  same  result  can  be  obtained  by  winding  a  coil  of  twenty  turns 
of  No.  24  wire,  threading  them  through  a  hole  bored  in  a  glass  plate 
and  supported  as  shown  in  Fig.  41.  The  hole 
in  the  glass  plate  can  be  bored  with  compara- 
tive ease  by  using  a  tube  of  iron  or  brass 
rotated  by  a  vertical  drill.  Clarnp  the  glass 
plate  between  two  boards,  with  a  hole  of  the 
size  of  the  tube  to  be  used  through  the  upper 
one,  and  feed  the  tube  with  fine  emery  or 
carborundum  moistened  with  spirits  of  tur- 
FIG.  41  pentine  in  which  camphor  has  been  dissolved. 

Since  an  arrow  is  used  conventionally  to  represent  the 
direction  in  which  an  electric  current  is  going,  a  small 
circle  with  a  dot  at  its  center,  to  represent  the  point  of 

the  arrow,  is  used  for  a  current ^. 

coming    toward    the    observer, 

while    a    circle    with    a    cross 

within  it,  to  represent  the  feathered  end  of  the  arrow,  is 

used  for  a  current  going  away  from  the  observer  (Fig.  42). 


46  ELECTRICITY 

GALVANOMETERS 

37.  Current,   Electro-motive    Force,   and   Resistance.  — 

Whenever  a  conductor  of  electricity  is  connected  to  the 
terminals' of  a  battery  or  other  electric  generator  an  elec- 
tric current  will  flow  along  the  conductor.  The  magni- 
tude of  the  current  will  depend  upon  the  relation  between 
the  electro-motive  force  generated  by  the  battery  and  the 
resistance  offered  by  the  conductor.  The  unit  of  current 
is  called  the  ampere. 

Electro -motive  force  is  analogous  to  water  pressure  in  a 
system  of  pipes  and  may  be  called  electrical  pressure. 
The  practical  unit  is  the  volt. 

The  resistance  of  a  conductor,  as  its  name  implies,  is 
the  resistance  offered  by  a  conductor  to  the  flow  of  the 
electric  current.  It  increases  as  the  length  of  the  con- 
ductor increases,  and  as  the  cross  section  diminishes.  It 
also  varies  with  the  material  used.  The  unit  is  the  ohm. 

These  definitions  are  given  to  enable  us  to  study  gal- 
vanometers intelligently  ;  the  more  complete  definitions 
will  be  left  for  consideration  later. 

38.  The  Principles  of  Galvanometers.  —  The  three  classes 
of  galvanometers  suggested  by  the  preceding  experiments 
depend  upon  the  following  principles  : 

1st.  That  a  magnetic  needle  will  be  deflected  when- 
ever an  electric  current  is  sent  through  a  wire  near  it. 

2d.  That  an  iron  core  will  be  drawn  toward  the  center 
of  a  coil  whenever  a  current  of  electricity  passes  through 
the  coil. 

3d.  That  any  coil  of  wire,  however  short,  becomes  a 
magnet  with  its  poles  lying  in  the  axis  of  the  coil  when- 
ever an  electric  current  is  sent  through  it,  and  hence  the 


GAL  VA  NOMETERS 


47 


coil,  if  properly  suspended,  will  be  deflected  in  the  pres- 
ence of  another  magnet. 

The  force  that  tends' to  keep  the  reading  of  the  galva- 
nometer at  the  zero  point  is  called  the  controlling  force, 
and  is  as  follows  in  the  three  classes  of  instruments : 

Class  1.  The  horizontal  component  of  the  earth's  mag- 
netism, or  a  bar  magnet  that  can  be  placed  in  any  desired 
position. 

Class  2.  Gravity  acting  upon  a  weight  at  one  end  of  a 
balance,  or  the  pull  of  a  spiral  spring. 

Class  3.  Either  the  tension  of  a  wire  suspending  the 
coil,  or  the  action  of  a  flat  spiral  spring  to  which  the  coil 
is  fastened. 

39.  The  Tangent  Galvanometer.  —  The  tangent  galva- 
nometer is  of  the  first  class.  In  order  that  the  law  of  the 
galvanometer  may  hold, 
the  needle  must  be  sup- 
ported in  the  middle  of 
the  vertical  coil,  and  the 
diameter  of  the  coil  must 
be  ten  or  twelve  times 
the  length  of  the  needle. 

The  general  form  of 
the  instrument  is  shown 
in  Fig.  43.  When  the 
galvanometer  is  in  use, 
the  plane  of  the  ring 
must  be  vertical  and  in 
the  magnetic  meridian. 

Figure  44  is  a  horizon- 
tal section  through  the 
middle  of  the  instrument,  which,  for  the  sake  of  simplicity, 


48 


ELECTRICITY 


FIG.  44 


is   supposed   to   have   but   a   single  turn  of  wire.     The 

circles  surrounding  the  wire  represent  the  magnetic  lines 

of  force. 

By  extending 
the  lines  of  force 
until  they  reach 
the  needle,  it  will 

be  seen  that  with  a  short  needle  the  deflecting  force  acts 

in  an  east-and-west  direction,  when  the  galvanometer  is 

placed  with  its  coil  in  the  magnetic  meridian. 

If  ab  (Fig.  45)  represents  the  deflecting  force  acting  on 

the  -ZV^end  of  the  needle,  the  component  of  this  force  that 

acts  at  a  right  angle  to  the  needle  will 

be  ab  cos  x,  in  which  x  is  the  angle  of 

the  deflection.     The  controlling  force 

is  ad  =  H,  and  when  the  needle  is  in 

equilibrium,  the  component  ae  =  H  sin 

x  is  equal  and  opposite  to  ac.     Hence 

we  have  ab  cos  x  =  If  sin  x,  and  ab  =  H 

tan  x.     Since  ab  is  proportional  to  the 

current,  ab  =  k  0  =ff  tan  x,  in  which  k 

is  a  constant  depending  upon  the  in- 
strument.      For    any    other    current 

C",    kC'  =ff  tan  x' \    hence  <?:<?'  = 

tan  x:  tan  x'.      This   means   that   the 

currents  passing  through  the  coil  of  a 

tangent  galvanometer  are  proportional, 

not  to  the  angle  of  the  deflection,  but  to  the  tangent  of 

that  angle. 

40.  The  Astatic  Galvanometer.  —  This  form  of  galva- 
nometer is  of  the  first  class,  and  is  used  for  the  detection 
of  small  currents.  It  is  used  in  what  are  called  "  nil "  or 


FIG.  45 


GALVANOMETERS  49 

zero  methods,  in  which  the  current  between  the  points  to 
which  the  galvanometer  is  connected  is  reduced  to  zero. 
Figure  46  is  a  diagram  of 
the  relative  positions  of 
the  coil  and  the  needle. 
The  suspended  part 
consists  of  two  magnetic 
needles  rigidly  fixed  to  £ 
a  vertical  piece  DH.  '  s- 


F 


D 


o 


H- 

These  needles  are  of  B 

V      ,,  FIG.  46 

practically     the      same 

magnetic  strength,  and  have  their  poles  opposite  to  each 
other.  The  coil  incloses  the  lower  needle,  passing  above 
and  below  it,  while  the  upper  one  acts  as  a  pointer,  being 
above  a  circular  scale,  represented  in  the  diagram  by  the 
line  FG-,  from  which  the  deflections  can  be  read. 

By  applying  the  law  of  deflection  to  the  effect  of  the 
branches  AE  and  BE  upon  the  upper  and  lower  needles 
respectively,  the  direction  of  the  deflection  will  be  deter- 
mined, and  the  reason  for  the  sensitiveness  of  the  gal- 
vanometer will  be  shown. 

41.  Reflecting  Galvanometers.  —  In  order  that  small 
currents  may  be  measured  accurately,  it  is  necessary  not 
only  that  a  small  current  shall  produce  a  large  deflection, 
but  that  a  small  deflection  shall  be  easily  read. 

These  results  are  obtained  in  the  reflecting  galvanometer, 
by  fixing  a  light  mirror  to  the  magnetic  needle  and  sus- 
pending the  movable  system  by  a  silk  or  quartz  fiber.  The 
reading  is  taken  by  directing  a  telescope  toward  the  mirror 
and  observing  in  it  the  reflections  from  a  fixed  scale.  The 
Thomson  and  Edelmann  galvanometers  are  familiar  exam- 
ples of  this  type. 

ELEC.    AND  MAG.  4 


50 


ELECTRICITY 


X- 


42.  The  D' Arsonval  Galvanometer.  —  This  form  of  gal- 
vanometer is  of  the  third  class ;  it  depends  upon  the 
principle  that  if  a  flat  coil  of  wire  is  suspended  with  its 

axis  perpendicular  to  a  strong 
magnetic  force,  it  will  be  deflected 
whenever  a  current  of  electricity 
is  passed  through  it.  The  rela- 
tion of  the  coil  to  the  magnetic 
field  is  shown  in  Fig.  47. 

The  coil  is  a  rigid  rectangular 
coil  wound  upon  a  copper  form, 
and  suspended  by  the  fine  wires 
AC  and  DB  between  the  points 
A  and  B.  NKS  is  a  permanent 
magnet  with  its  poles  at  N  and  S. 
I  is  a  soft  iron  cylinder  fixed 
between  the  poles,  helping  to 
make  a  strong  magnetic  field 
across  the  air  gap  in  which  the  coil  moves. 

Figure  48  shows  an  enlarged  horizontal  cross  section  on 
the  line  XY  of  Fig.  47.  By  the 
conventions  mentioned  in  Section  36 
to  represent  the  direction  of  the 
current  in  the  coil,  the  directions 
of  the  current  in  the  two  figures 
agree,  and  the  poles  N'S1  of  the  sus- 
pended coil  will  be  as  shown  in  the 
figure.  By  applying  the  law  of  mu- 
tual action  between  magnetic  poles  it 
is  seen  that  the  poles  of  the  coil  will 
move  into  the  position  ns.  A  change 
in  the  direction  of  the  current  changes  the  polarity  of  the 
coil  and  consequently  the  direction  of  the  deflection. 


FIG.  48 


GALVANOMETERS  51 

The  delicacy  of  the  instrument  depends  upon  the 
strength  of  the  field  of  the  permanent  magnet,  the  number 
of  turns  in  the  suspended  coil,  arid  the  torsion  of  the  wire 
by  which  it  is  suspended. 

This  is  called  a  "deadbeat"  instrument,  i.e.  one  that 
comes  to  rest  quickly  without  a  series  of  diminishing 
vibrations.  This  result  is  brought  about  by  the  current 
which  is  induced  in  the  coil  when  it  moves,  and  which 
opposes  this  motion. 

43.  The  Differential  Galvanometer.  —  A  galvanometer 
is  said  to  be  wound  differentially  when  it  is  supplied 
with  two  coils  of  equal  resistance,  so  wound  that  when 
the  same  current  passes  through  each,  there  will  be  no 
deflection  of  the  needle. 

JC 

The  relative  positions 
of  the  coils  and  needle 
are  shown  in  Fig.  49. 
This  method  is  used 
in  the  measurement  of 
small  resistances,  and  ?/ 

FIG.  49 

since  it  is  a  zero  method, 

any  form  of  cell  can  be  used,  even  if  it  does  not  give  a 

current  of  constant  value. 

In  order  to  adjust  the  coils  of  a  differential  galva- 
nometer, they  must  be  brought  to  the  same  resistance  by 
being  balanced  against  each  other  in  the  arms  of  a  Wheat- 
stone  bridge.  To  bring  them  into  the  proper  position 
when  the  same  current  is  passing  through  each,  they 
must  be  coupled  in  series  in  such  a  way  that  they  tend 
to  turn  the  needle  in  opposite  directions,  and  then  moved 
nearer  to  the  needle  or  farther  from  it  until  the  needle 
stands  at  zero  with  any  current.  When  the  proper  posi- 


52  ELECTRICITY 

tion  of  the  coils  has  been  found  in  this  way,  the"y  are 
coupled  as  in  Fig.  49,  with  one  of  the  resistances  to  be 
compared  between  the  binding  posts  A  and  B,  and  the 
other  between  the  posts  0  and  D.  If  the  coils  are  not 
movable,  a  turn  or  more  can  be  unwound  from  the  coil 
giving  the  greatest  magnetic  effect  until  a  balance  is 
obtained,  and  then  the  wire  so  unwound  can  be  coiled 
in  the  base  of  the  instrument. 

44.  The  Ballistic  Galvanometer.  —  A  ballistic  galvanom- 
eter is  one  that  is  used  in  cases  in  which  the  current 
lasts  for  a  very  short  time  only,  as  in  the  discharge  of  a 

condenser.  The  quantity  of  electricity 
that  passes  in  the  current  is  indicated  by 
the  maximum  swing,  or  "  throw "  of  the 
needle.  In  order  that  the  throw  may  be 
proportional  to  the  quantity  of  electricity, 
there  must  be  as  little  resistance  to  the 
movement  of  the  needle  as  possible  and 
it  must  have  a  long  period 
of  vibration.  The  coils 
are  usually  wound  for  high 
resistance,  while  the  needle 
is  heavy  and  frequently 
bell-shaped  as  in  Fig.  50.  Deflections  are  read  by  the 
reflections  of  a  scale  in  the  mirror  M. 

45.  Figure  of  Merit.  —  In  order  that  the  galvanometer 
shall  be  of  value  as  a  measuring  instrument,  the  relation 
between  the  current  and  the  deflection  produced  by  it 
must  be  known.     The  usual  method  is  to  determine  ex- 
perimentally the  value  of  the  current  required  to  produce 
one  scale  division.     This  current  expressed  in  amperes 


^      ftMMlQM 


AMMETERS;    VOLTMETERS  53 

is  called  the  figure  of  merit  of  the  galvanometer.  It  is 
expressed  either  as  a  decimal  or  as  a  number  multiplied 
by  10  with  a  negative  exponent. 

A  small  figure  of  merit  indicates  a  sensitive  galva- 
nometer. The  difference  of  potential  at  the  terminals  of 
the  galvanometer  corresponding  to  one  scale  division,  or 
its  sensitiveness,  may  be  found  by  multiplying  its  resist- 
ance by  the  figure  of  merit. 

46.  Ammeters.  —  An  ammeter  is  a  form  of  galvanometer 
used  to  measure  the  electric,  current.     These  instruments 
are  calibrated  to  read  directly  in  amperes.      They  are 
coupled  in  series  in  the 

circuit,  the  current  of 
which  is  to  be  measured, 
as  shown  in  Fig.  51. 
Their  coils  are  conse- 
quently made  of  few  turns  FlG  51 
of  large  wire  in  order 

that  the  resistance  may  be  small.  -  The  Idnd  of  ammeter 
used  in  any  circuit  should  be  such  that  its  introduction 
into  the  circuit  shall  change  the  current  as  little  as 
possible. 

EXPERIMENT  40.  —  To  classify  ammeters. 

Apparatus.  —  Ammeters  of  different  makes ;  cells  ;  and  a  switch. 

Manipulation.  —  Couple  each  ammeter  in  turn  to  the  cells,  with  the 
switch  in  the  circuit.  Examine  the  construction  and  test  the  deflec- 
tion of  each. 

Determine  the  class  of  galvanometers  to  which  each  instrument 
belongs. 

47.  Voltmeters.  — A  voltmeter  is  a  form  of  galvanome- 
ter used  to  measure  the  difference  of  potential  between 
two  points.     It  is  calibrated  to  read  in  volts,  and  is  coupled 
as  a  shunt  to  the  circuit  at  the  two  points  between  which 


54  ELECTRICITY 

the  potential  difference  is  to  be  measured.     This  form  of 

coupling  is  shown  in  Fig.  52. 

In  order  that  the  current  passing  through  the  instru- 
ment may  be  small,  the 
coils  are  wound  with  fine 
wire.  This  means  that 


o|  little  change  will  be  made 

in  the  potential  difference 
FlG>  52  of  the  two  points  by  put- 

ting the  voltmeter  in  connection  with  them. 

EXPERIMENT  41. — rTo  classify  voltmeters. 

Apparatus.  —  Voltmeters  of  different  makes;  a  resistance  coil; 
cells;  and  a  switch. 

Manipulation.  —  Couple  the  cells  in  series  to  the  switch  and  resist- 
ance coil,  which  should  have  a  resistance  of  at  least  1000  ohms. 
Connect  each  voltmeter  in  turn  as  a  shunt  to  the  terminals  of  the 
resistance  coil.  Examine  the  construction  and  test  the  deflection 
of  each. 

Determine  the  class  of  galvanometer  to  which  each  instrument 
belongs. 

BATTERIES 

48.  Galvanic  Batteries. — The  galvanic,  or  voltaic,  cell 
is  an  electric  generator  in  which  the  current  is  the  result 
of  the  physical  relations  between  the  different  materials  of 
which  the  cell  is  composed.  When  a  number  of  these  cells 
are  coupled  together  they  form  a  battery.  A  cell  can  be 
made  by  inserting  in  a  liquid  any  two  solids,  usually  metals, 
upon  which  the  liquid  acts  with  different  intensities. 

The  accompanying  table  is  arranged  in  such  a  way  that 
if  the  substances  are  placed  in 

dilute  sulphuric  acid,  each  will        l-  zinc  6-   Copper 

be  electro-positive  to  the  ones       2'  Tin  7>  Silver 


following  it  and  electro-negative 
to  those  preceding  it.     Thus  it 


3.  Lead  8.    Gold 

4.  Iron  9.    Platinum 

5.  Nickel        10.    Graphite 


BATTERIES 


55 


will  be  seen  that  iron  is  electro-positive  to  copper  and 
electro-negative  to  zinc.  The  order  given  in  the  table 
does  not  hold  for  other  liquids.  In  potassium  sulphide, 
for  example,  copper  is  electro-positive  to  iron. 

EXPERIMENT  42.  —  A  partial  verification  of  the  preceding  table. 

Apparatus. —  A  battery  jar  half  full  of  dilute  sulphuric  acid;  plates 
of  copper,  iron,  and  zinc ;  strips  of  wood ;  connecting  wires ;  and  a 
voltmeter. 

Manipulation.  —  Drill  two  holes  in  the  end  of  each  plate,  and  screw 
them  to  the  strips  of  wood.  Attach  wires  to  each  plate  as  shown  in 
the  figure.  Test  the  voltage  of  each  pair  by 
coupling  to  the  voltmeter. 

Arrange  the  metals  in  the  order  indicated  by 
their  difference  of  potential.  Is  the  order  the 
same  as  that  in  the  table?  Does  the  difference 
in  voltage  between  the  copper  and  the  zinc  equal 
the  sum  of  differences  between  the  copper  and 
the  iron,  and  the  iron  and  the  zinc  ? 

NOTE.  —  If  metal  A  is  electro-positive  to  metal 
B,  when  placed  in  a  liquid,  the  current  passes  from  A  to  B  in  the 
liquid,  and  from  B  to  A  in  the  external  circuit. 


49.  The  Gravity  Cell.  — 


FIG.  54 


This  cell  consists  of  a  glass  jar 
in  the  bottom  of  which  is 
placed  a  copper  plate,  generally 
made  of  thin  copper  spread  out 
to  give  greater  surface,  around 
which  are  packed  crystals  of 
copper  sulphate.  Water  is 
poured  into  the  jar  to  make 
a  solution  of  the  copper  sul- 
phate, and  upon  this  is  poured 
a  solution  of  zinc  sulphate,  or 
dilate  sulphuric  acid.  Sus- 
pended from  the  edge  of  the 


56  ELECTRICITY 

jar  is  a  zinc  plate,  frequently  in  a  form  that  gives  the  cell 
the  name  of  the  crowfoot  cell.  The  general  name  of  this 
cell  is  derived  from  the  fact  that  the  copper  sulphate 
solution,  being  heavier  than  the  zinc  sulphate,  is  kept 
separated  from  it  by  the  action  of  gravity. 

As  a  result  of  the  action  that  takes  place  in  the  cell  the 
zinc  plate  is  destroyed,  and  the  zinc  sulphate  is  increased 
in  amount,  while  the  copper  from  the  copper  sulphate  is 
deposited  as  metallic  copper  on  the  copper  plate.  In 
chemical  symbols  this  action  is  expressed  as  follows : 
Zn  +  ZnSO4  +  CuSO4  +  Cu  =  2  ZnSO4  +  2  Cu. 

By  substituting  the  atomic  weights  of  the  elements  in 
this  formula,  we  can  find  how  much  copper  sulphate  is 
needed  to  use  up  a  given  quantity  of  zinc. 

The  gravity  cell  gives  a  nearly  constant  voltage  and 
steady  current  and  is  much  used  on  telegraph  lines.  The 
copper  terminal  is  positive  to  the  zinc  terminal,  and  in 
the  external  circuit  the  current  goes  from  the  copper 
to  the  zinc.  This  means  that  the  positive  terminal  is 
attached  to  the  electro-negative  plate  and  the  negative 
terminal  to  the  electro-positive  plate. 

50.  The  Leclanche  Cell.— This  cell 
consists  of  a  glass  jar  in  which 
is  placed  a  porous  cup  containing 
a  carbon  plate  embedded  in  man- 
ganese dioxide  and  gas  carbon,  both 
in  small  pieces.  The  porous  cup  is 
sealed  after  the  contents  have  been 
well  packed  together.  After  the 
porous  cup  is  placed  in  the  glass  jar 
a  solution  of  sal  ammoniac  is  poured 
FIG.  55  in  until  the  jar  is  two  thirds  full,  and 


BATTERIES  57 

a  zinc  rod  is  placed  in  the  solution  by  the  side  of  the  por- 
ous cup.  This  cell  is  an  open-circuit  cell,  and  is  used 
when  the  current  is  wanted  for  a  short  time  only,  as  in 
electric  bell  lines.  When  a  cell  is  capable  of  giving  a 
steady  current  for  some  time,  like 
the  gravity  cell,  it  is  called  a  closed- 
circuit  cell. 

51.  The  Potassium  Bichromate 
Cell.  —  A  common  form  of  this  cell 
is  shown  in  Fig.  56.  The  two  out- 
side plates  are  of  carbon  and  are 
fixed  to  the  cover  of  the  cell.  The 
middle  plate  is  of  zinc  and  can  be 
lowered  into  the  liquid  or  raised 
from  it  and  clamped  in  place  by  the 
middle  rod.  As  the  action  goes  on 
in  the  cell  whenever  the  zinc  is  in 
the  liquid,  the  plate  should  be  raised 
except  when  the  cell  is  in  use. 

A  satisfactory  formula  for  the  liquid  is : 

Pulverized  potassium  bichromate  .  .  1  Ib. 
Strong  sulphuric  acid  .  .  .  .  .  2  Ib. 
Water  .  .  .  .,  .  ...  .  .  12  Ib. 

The  bichromate  must  be  added  to  the  acid  with  con- 
stant stirring,  after  which  the  mixture  is  to  be  poured 
slowly  into  the  water,  also  with  constant  stirring.  An- 
other formula,  more  easily  made  up,  is  as  follows : 

Commercial  chromic  acid      .     .     160  grams 
Water      .     .     ....     .     .  1420  c.c. 

Sulphuric  acid  .     .  "-.     .    *".     .       90  c.c. 

Dissolve  the  chromic  acid  in  the  water  and  then  add 


58 


ELECTRICITY 


slowly  the  sulphuric  acid,  stirring  the  mixture  with  a 

glass  rod. 

This  is  a  convenient  form  of  cell  when  a  strong  current 

is  needed  for  a  short  time.  A  number  of  these  cells  are 
frequently  arranged  in  such  a  way  that 
the  zincs  can  all  be  raised  and  lowered 
at  the  same  time,  thus  forming  a  plunge 
battery. 

52.  The  Dry  Battery.  —  A  convenient 
form  of  portable  cell  is  what  is  called 
the  dry  battery.  The  zinc  plate  forms 
the  outer  cup  of  the  cell,  and  the  carbon 
plate  is  packed  in  the  middle,  extending 
above  the  contents  of  the  cell.  This  is 
a  useful  cell  when  the  current  is  wanted 
but  a  little  while  at  a  time,  and  forms  a 
ready  means  of  obtaining  a  battery  of 
high  electro-motive  force  by  coupling  a 
FIG.  57  number  of  these  cells  in  series. 

EXPERIMENT  43.  —  To  examine  different  kinds  of  cells. 

Apparatus.  —  Cells  of  the  above  types  ;  a  voltmeter. 

Manipulation.  —  Measure  the  voltage  of  each  cell  by  coupling  a 
voltmeter  directly  to  its  terminals,  take  a  record  of  each,  and  make  a 
list  of  the  voltages  of  the  different  classes. 

Observe  whether  the  cells  of  each  class  have  a  common  voltage. 
The  voltage  of  these  cells  should  be  taken  later  in  the  year  after  they 
have  had  considerable  laboratory  use,  and  the  readings  compared  with 
those  now  taken. 

EXPERIMENT  44.  —  To  study  the  effect  upon  the  voltage  of  a  cell, 
produced  by  taking  a  continuous  current  from  it. 

Apparatus.  —  One  open-circuit  and  one  closed-circuit  cell;  two  low- 
resistance  coils ;  two  voltmeters  ;  and  two  switches. 

Manipulation.  —  Couple  each  cell  with  a  low-resistance  coil  and  a 


BATTERIES  59 

switch,  and  couple  a  voltmeter  to  the  terminals  of  each  cell.  Read 
the  voltage  of  each  cell  before  the  switch  has  been  closed,  and  for  each 
five  minutes  afterward  as  long  as  it  seems  to  be  desirable,  opening 
the  switch  each  time  just  long  enough  to  take  the  reading. 

From  the  record  made  for  each  cell  make  a  curve  that  shall  show 
the  relation  between  the  voltage  of  the  cell  and  the  time  of  observa- 
tion. The  form  of  the  curve  should  show  clearly  the  different  effects 
of  polarization  in  the  two  cells. 

EXPERIMENT  45.  — -To  find  the  voltage  of  cells  coupled  in  series. 

Apparatus.  —  Four  or  five  cells  of  the  same  kind;  a  voltmeter. 

Manipulation.  —  Take  the  voltage  of  each  cell  separately.  Couple 
the  cells  in  series,  taking  first  two,  then  three,  and  so  on  until  the 
whole  number  is  used,  and  take  the  voltage  of  each  set. 

The  results  of  this  experiment  should  show  that  when  N  cells  are 
coupled  in  series,  their  combined  voltage  is  the  sum  of  their  voltages 
taken  separately.  If  the  cells  have  a  uniform  voltage,  the  voltage  of 
N  cells  will  be  N  times  the  voltage  of  one. 

EXPERIMENT  46.  —  To  find  the  voltage  of  cells  coupled  in  parallel. 

Apparatus.  —  The  cells  and  voltmeter  used  in  Experiment  45. 

Manipulation.  —  Couple  the  cells  in  parallel  instead  of  in  series  as 
before,  and  take  the  voltage  of  each  set. 

The  results  of  this  experiment  should  show  that  the  voltage  of  any 
number  of  cells  coupled  in  parallel  is  the  same  as  the  voltage  of  a 
single  cell. 

The  results  of  this  and  the  previous  experiment  are  as 
true  for  dynamos  as  for  cells. 

53.   The  Electro-motive  Force  of  a  Cell.  — EXPERIMENT  47.  — 

Does  the  size  determine  the  voltage  of  a  cell  ? 

Apparatus.  —  A  potassium  bichromate  cell  and  a  voltmeter. 

Manipulation.  —  Couple  the  voltmeter  to  the  cell  and  push  down 
the  rod  carrying  the  zinc  far  enough  so  that  the  zinc  will  just  touch 
the  liquid.  Read  the  voltmeter  and  make  a  record  of  the  reading. 
Push  down  the  zinc  a  half  inch  more,  take  the  reading,  and  make  a 
record.  Repeat  the  process  until  the  zinc  is  entirely  submerged. 

The  results  of  this  experiment  show  that  the  size  of  a  cell  does  not 
determine  its  voltage.  By  referring  to  the  results  of  Experiment  43, 


60  ELECTRICITY 

we  see  that  different  cells  have  different  voltages ;  hence  we  may  say 
that  the  voltage  of  a  cell  does  not  depend  upon  its  size,  but  upon  the 
kind  of  plates  used  and  the  solution  in  which  they  are  used. 

QUESTIONS   AND  PROBLEMS 

1.  The  controlling  force  in  a  certain  galvanometer  is  the  earth's 
magnetism.     In  what  position  should  the  coil  be  when  in  use  ?     Why  ? 

2.  Suppose  an  electro-magnet  is  to  be  used  in  a  circuit  in  which 
there  is  a  high  resistance  but  a  small  current ;  would  you  wind  it  with 
fine  or  with  coarse  wire  ?     Why  ? 

3.  Make  drawings  for  the  connections  of  a  "single  stroke"  bell, 
that  is,  one  that  will  strike  only  once  when  the  circuit  is  closed. 

4.  Make  a  drawing  of  the  end  of  an  ordinary  horseshoe  electro- 
magnet, showing  the  direction  of  the  winding  and  the  resulting  polar- 
ity of  each  core.     Do  the  same  for  the  electro-magnet  of  a  polarized 
bell.     Compare  the  two  drawings. 

5.  What  is  the  difference  between  a  galvanometer  and  a  galvano- 
scope  ? 

6.  A  tangent  galvanometer  gives  a  deflection  of  8  degrees ;  what 
will  be  the  deflection  when  the  current  strength  is  doubled? 

7.  A  certain  galvanometer  has  a  figure  of  merit  of  .015,  and  its 
resistance  is  .023  ohm.     What  difference  of  potential  at  its  terminals 
is  necessary  to  produce  a  deflection  of  one  scale  division? 

8.  Suppose  you  have  a  current  passing  through  a  given  resistance ; 
show  the  effect  of  coupling  the  voltmeter  in  series  with  the  resistance 
instead  of  at  its  terminals. 

9.  How  much  copper  sulphate  must  be  taken  in  a  gravity  cell  to 
use  up  a  zinc  plate  weighing  3  Ib.  ? 

10.  An  incandescent  -lamp  in  the  hall  of  a  house  is  to  be  turned  on 
or  off  by  a  switch  at  the  front  door,  and  also  by  one  on  the  second 
floor.  Show  by  a  drawing  the  arrangement  of  switches,  lamp,  and 
connecting  wires.  Verify  the  drawing  by  constructing  a  line  that 
will  fulfill  the  conditions. 

RESISTANCE 

54.  Electrical  Contacts.  —  In  making  the  contacts  for  an 
electrical  circuit,  great  care  should  be  taken  that  they  are 
firm  and  bring  the  parts  into  a  real  metallic  contact. 


EESISTANCE  61 

When  two  wires  are  to  be  connected  permanently  they 
should  be  soldered  and  not  twisted  together.  Twisting 
the  end  of  a  wire  to  make  a  contact  not  only  does  not 
make  a  good  contact,  but  it  spoils  the  end  of  the  wire  for 
future  use. 

EXPERIMENT  48.  —  To  show  the  value  of  a  good  contact. 

Apparatus.  —  A  brass  chain  fastened  at  one  end  and  held  at  the 
other  by  one  end  of  a  lever,  as 
in    Fig.    58;    cell;     and    gal- 
vanometer. 

Manipulation.  —  Couple  the 
chain,  cell,  and  galvanometer 

in     series.       Notice    the     de- 

r  IG.  DO 
flection  of   the  galvanometer, 

first  when  the  chain  is  hanging  loose,  and  then  when  it  is  drawn  tight 
by  pulling  down  on  the  free  end  of  the  lever. 

Does  the  poor  contact  made  by  the  chain  when  loose  increase  or 
decrease  the  current  flowing  through  the  galvanometer? 

55.  Electrical  Resistance. — The  resistance  of  an  elec- 
trical conductor  depends  upon  three  things :  its  length, 
its  cross  section,  and  its  material.  The  relation  that  each 
of  these  holds  to  the  resistance  will  be  shown  in  the  follow- 
ing experiment. 

EXPERIMENT  49.  —  To  show  how  the  resistance  of  a  conductor 
varies. 

Apparatus.  —  Insulated  copper  wire  No.  18  and  No.  30;  German 
silver  wire  No.  30 ;  cells  ;  and  a  galvanometer. 

Manipulation.  —  Cut  from  the  No.  18  wire  a  piece  10  ft.  long, 
and  couple  it  in  series  with  the  cells  and  the  galvanometer.  Read 
the  deflection  of  the  galvanometer.  Repeat,  using  a  piece  of  copper 
wire,  No.  18,  30  ft.  long,  and  then  a  piece  of  copper  wire,  No.  30,  30  ft. 
long.  Do  the  same  with  a  piece  of  the  German  silver  wire  30  ft.  long. 

Since  the  deflection  of  the  galvanometer  increases  with  an  increase 
of  the  current,  and  since  the  current  decreases  with  an  increase  of  the 
resistance,  the  results  of  the  experiment  should  show  that  an  increase 


62  ELECTRICITY 

in  the  length  of  a  wire  increases  its  resistance  ;  that  an  increase  in  its 
diameter  decreases  its  resistance  ;  and  that  changing  from  a  copper 
wire  to  a  German  silver  wire  of  the  same  length  and  diameter  in- 
creases the  resistance. 

56.  Formula  for  the  Resistance  of  a  Wire.  —  The  rela- 
tion between  the  length,  diameter,  and  material  of  a  wire 
and  its  resistance  may  be  expressed  by  a  formula. 

Let  R  equal  resistance. 

Let  L  equal  length. 

Let  A  equal  area  of  cross  section. 

Let  D  equal  diameter. 

Let  k  equal  a  constant  depending  upon  the  material  of 
the  wire,  and  called  its  specific  resistance.  This  is  the 
resistance  of  a  cube  of  the  material  one  unit  in  length. 

The  resistance  will  then  be  expressed  as  follows  : 


Since  the  areas  of  cross  section  of  two  wires  are  directly 
proportional  to  the  squares  of  their  diameters,  the  formula 

can  be  written  R  =  k  —  •     In  a  second  wire  in  which  the 

L' 

length  is  L'  it  becomes  R  =  k  —      Hence   we  can  write 

R  :  R'  =  L  :  L'.  Stated  as  a  law  this  becomes  :  In  wires 
of  the  same  diameter  and  material  the  resistances  are 
directly  proportional  to  the  lengths.  In  the  same  way  we 
can  derive  R  :  R  =  D'2  :  D2,  and  R  :  R'  =  k  :  V. 

57.  Ohm's  Law.  —  The  definite  relation  existing  between 
electro-motive  force,  resistance,  and  current  was  investi- 
gated in  a  series  of  careful  experiments  by  Ohm  in  1827. 
Using  the  same  conductor,  he  proved  not  only  that  the 
current  varies  with  the  electro-motive  force,  but  that  this 


RESISTANCE 


63 


variation  is  in  a  direct  proportion.  This  means  that  the 
resistance  of  a  conductor  is  the  ratio  of  the  electro-motive 

XT 

force  to  the  current.     The  law  as  usually  stated  is  C=  — 

E 

From  this  two  other  forms  can  be  derived :    R  =  —,  and 

C 

E  —  RO.  This  is  the  foundation  formula  for  these  rela- 
tions, and  should  be  made  so  familiar  that  it  can  be  recog- 
nized in  its  various  forms. 

58.   Resistance  Boxes.  —  A  resistance  box  is  a  box  con- 
taining coils  of  resistance  wire  with  their  ends  connected 


FIG.  59 

to  terminals  in  such  a  way  that  they  can  be  thrown  into  a 

circuit,  or  out  of  it,  at  will.     Figure  59  shows  a  common 

form  of  resistance  box,  while  the  method 

of  winding  the  coil  double  so  that  it  shall       -»   r^7   A 

be   non-inductive,    and    of    connecting    its 

ends,  is  shown  in  Fig.  60.     In  using  the 

plug  resistance  box  care  should  be  taken 

to  put  the  plugs  in  with  a  slight  twist  so 

that  there  shall  be  no  resistance  introduced 

by  poor  contact.  FlG>  00 


64 


ELECTRICITY 


59.  The  Measurement  of  Resistance  ;  the  Substitution 
Method.  —  There  are  a  number  of  ways  in  which  the  resist- 
ance of  a  conductor  can  be  measured.     One  of  the  simplest 
of  these  is  the  method  of  substitution.     It  is  not  an  accu- 
rate method,  unless  the  contacts  are  very  carefully  made, 
but  will  give  a  close  approximation. 

EXPERIMENT  50.  —  To  measure  a  resistance  by  the  substitution 
method. 

Apparatus.  —  A  galvanometer;  resistance  box;  two  or  more  cells; 

the  substitution  board  shown  in  the  figure ;  and  the  wire  to  be  tested. 

Manipulation.  —  Couple  the  resistance  box   and   the   wire   to  be 

tested  to  the  cells  and  galvanometer  by  means  of  the  substitution 

board,  as  shown  in 
Fig.  61.  Turn  the 
switch  so  that  the 
current  will  pass  first 
through  the  coil  cir- 
cuit, and  observe  the 
deflection  of  the  gal- 
vanometer. Turn 
the  switch  so  that 
the  current  will  pass 
through  the  box  cir- 
cuit, and  regulate 
the  resistance  in  the 
box  so  that  the  deflec- 
tion of  the  galvanom- 
eter shall  be  nearly 
FlG-  61  what  it  was  in  the 

first  circuit.  Throw  the  current  from  one  circuit  to  the  other,  chan- 
ging the  resistance  in  the  box  until  the  deflection  of  the  galvanometer 
does  not  change  on  throwing  the  switch.  When  this  condition  is 
found,  the  reading  of  the  box  is  the  resistance  of  the  coil. 

60.  The  Fall  of  Potential  along  a  Wire.  —  Whenever 
there  is  an  electric  current  passing  along  a  wire,  there 
will  be  a  fall  of  potential  along  it  that  will  be  dependent 


RESISTANCE 


65 


upon  the  resistance  of  the  wire.  If  this  is  of  homogeneous 
material  and  of  uniform  cross  section,  the  resistance  will  be 
the  same  for  equal  lengths,  and  the  fall  of  potential  will 
be  proportional  to  the  length.  In  order  to  measure  this 
fall  of  potential  the  apparatus  shown  in  Fig.  62  may  be 
used. 


19     18      1 


FIG.  62 

EXPERIMENT  51.  —  To  determine  the  fall  of  potential  along  a  wire. 

Apparatus.  —  A  board  with  a  German  silver  or  iron  wire  2  m. 
long  stretched  between  the  points  C  and  D\  a  number  of  cells; 
a  voltmeter;  an  ammeter;  a  switch  ;  and  connecting  wires. 

Manipulation.  —  Divide  the  distance  CD  into  equal  parts,  as  at  1, 
2,  etc.  Couple  the  wire,  cells,  ammeter,  and  switch  in  series.  Couple 
one  terminal  of  the  voltmeter  to  the  point  C,  as  shown,  and  its  other 
terminal  to  the  points  /),  19,  18,  etc.,  consecutively.  Read  the  am- 
meter and  voltmeter  at  the  same  time  and  tabulate  the  results.  If 
the  cells  are  of  a  kind  that  polarize  easily,  a  variable  resistance  should 
be  coupled  in  series  with  the  wire,  in  order  to  keep  the  current  of 
uniform  value.  A  fairly  good  result  can  be  obtained  by  omitting  the 
ammeter  and  using  the  current  only  long  enough  at  a  time  to  read 
the  voltmeter. 

Make  a  curve  showing  the  relation  between  the  length  of  a  wire 
and  the  fall  of  potential  along  it,  when  a  uniform  difference  of  poten- 
tial is  maintained  at  its  ends. 

61.  The  Measurement  of  Resistance ;  the  Fall  of  Potential 
Method.  —  By  applying  Ohm's  law  to  the  case  of  a  current 

ELEC.    AND    MAG.  — 5 


66 


ELECTRICITY 


flowing  along  a  wire,  we  see  that  the  current  that  passes 
depends  upon  the  resistance  of  the  wire  and  the  difference 
of  potential  at  its  ends.  This  difference  of  potential  at 

different  points 
is,  as  the  pre- 
vious experiment 
shows,  the  fall  of 
potential  along 
the  wire.  In 
order  to  measure 
the  resistance  of 
a  conductor  by 
this  method,  both 
an  ammeter  and 
a  voltmeter  must 
be  used.  Fig- 
ure 63  shows  the 
coupling  of  the 

ammeter,  voltmeter,  cells,  and  resistance  to  be  measured. 
The  ammeter  is  coupled  in  series  with  the  resistance,  to 
measure  the  current,  while  the  voltmeter  is  put  in  as  a 
shunt  to  the  coil,  contact  being  made  at  its  terminals. 

EXPERIMENT  52.  —  To  measure  resistance  by  the  fall  of  poten- 
tial method. 

Apparatus. — An  ammeter;  voltmeter;  switch;  cells;  and  several 
coils  of  wire. 

Manipulation.  —  Couple  the  apparatus  as  shown  in  the  figure 
above.  Read  the  instruments  simultaneously,  and  compute  the  resist- 
ance of  each  coil  from  the  expression 


FIG.  63 


This  method  is  a   convenient  one   for  practical   work 
in  electrical  stations,  since  it  requires  only  the  apparatus 


RESISTANCE 


67 


with  which  every  station  is  provided.  With  sensitive 
instruments  it  is  a  rapid  and  accurate  method.  The 
resistance  of  the  voltmeter  should  be  so  high  that  the  cur- 
rent that  passes  through  it  is  very  small,  so  small  in  fact 
that  the  reading  of 
the  ammeter  may  be 
taken  as  the  true 
value  of  the  current 
in  the  coil.  If  the 
resistance  of  the  volt- 
meter is  small,  it  can 
still  be  used,  but  must 
be  coupled  to  the 
terminals  of  the  am- 
meter and  coil  in 
series  as  shown  in 
Fig.  64.  The  resist- 
ance measured  with  this  coupling  will  be  the  sum  of  the 
resistances  of  the  coil  and  the  ammeter.  The  resistance 
of  the  ammeter  is  usually  known  and  can  be  subtracted 
from  the  sum  to  obtain  the  required  resistance. 

EXPERIMENT  53.  —  To  show  the  influence  of  the  voltmeter  resist- 
ance. 

Apparatus.  — A  coil  of  wire;  an  ammeter;  and  two  voltmeters,  one 
of  high  and  one  of  low  resistance. 

Manipulation.  —  Measure  the  resistance  of  the  coil  by  the  fall  of 
potential  method,  with  the  high -re  si  stance  voltmeter,  and  then  with 
the  low-resistance  voltmeter,  using  the  coupling  of  Fig.  63.  Explain 
the  difference  in  the  results.  Measure  again  with  the  low-resistance 
voltmeter,  using  the  method  of  Fig.  64.  Explain  the  difference 
between  this  result  and  that  of  the  last  measurement. 

62.  The  Wheatstone  Bridge.  —  If  an  electric  current  is 
going  from  the  point  A  to  the  point  5,  through  the  two 


FIG.  64 


68 


ELECTRICITY 


y  i 
<        III) 

V 

\ 

\ 

11  1 

IT 

paths  AxB  and  AyB,  in  Fig.  65,  it  is  evident  that  there 
is  the  same  fall  of  potential  in  each  branch,  since  they 
begin  and  end  at  the  same  point.     If  a  point  x  in  the 
x  upper  branch  is  con- 

nected by  a  conduct- 
ing wire  to  some  point 
of  the  lower  branch, 
as  y,  the  direction  of 
the  current  in  the 
wire  xy  will  depend 
upon  the  difference  of 
FlG'  65  potential  between  the 

points  x  and  y.  If  the  point  is  chosen  at  z  and  the  fall 
of  potential  from  A  to  z  is  less  than  from  A  to  x,  then  the 
current  will  go  from  z  to  x.  If  the  point  is  chosen  at  w, 
so  that  the  fall  of  potential  from  A  to  w  is  greater  than 
that  from  A  to  #,  the  current  will  go  from  x  to  w.  It  is 
evident  that  a  position  may  be  chosen  such  that  the  fall 
of  potential  from  A  to  y  will  be  the  same  as  from  A  to  x. 
When  this  position  is  found,  there  will  be  no  current  in 
the  conductor  xy.  The  relation  between  the  potential 
differences  at  the  several  points  can  now  be  written  : 

The  potential  difference  between  A  and  x  _ 
The  potential  difference  between  A  and  y 

The  potential  difference  between  x  and  B 
The  potential  difference  between  y  and  B 

We  have  already  learned  that  potential  differences  in 
conductors  are  proportional  to  their  resistances  ;  hence  we 
can  state  the  proportion  : 

The  resistance  of  Ax  _The  resistance  of  xB 
The  resistance  of  Ay     The  resistance  of  yB 


THE    WHEATSTONE  BRIDGE 


69 


Or,  letting  r,  r\  r",  r'"  represent  the  various  resistances, 


r  :  r  =  r    :  r 

If  we  substitute  a  wire  of  uniform  cross  section  for  the 
lower  branches,   as  in  Fig.    66,   the  proportion  becomes 

r:Z=r':Z'; 
whence       rl'  =  r'l. 

By  putting  a  galvanometer 
Q-  in  the  conductor  xy,  the 
position  in  which  there  is  no 
difference  of  potential  between 
x  and  y  is  determined  when 
there  is  no  deflection  of  the 
galvanometer. 

One  form  given  to  the  Wheatstone  bridge  for  practical 
work  is  shown  in  diagram  in  Fig.  67.     In  this  form  the 


FIG.  67 

wire  A  C  is  a  meter  long  and  is  fastened  to  the  base  of  the 
instrument  at  the  points  A  and  C.  This  wire  forms  one 
side  of  a  rectangle,  the  other  sides  of  which  are  formed  by 
a  copper  strap  which  has  two  gaps  in  it  at  EF  and  TH. 
One  of  these  gaps  is  bridged  by  the  resistance  to  be  meas- 


70  ELECTRICITY 

ured,  and  the  other  by  the  resistance  box.  The  battery  is 
connected  at  the  points  L  and  Jf,  while  the  galvanometer 
is  coupled  permanently  at  JV,  contact  with  the  wire  being 
made  by  the  key  K.  By  referring  to  Figs.  66  and  67, 
we  see  that  Ml'  =  Bl ;  i.e.  the  products  of  the  cross  multi- 
plications of  the  branches  of  the  bridge  are  equal.  While 
this  is  theoretically  true  for  any  values  of  I  and  Z',  it  is 
much  better  practice  to  keep  the  key  as  near  the  middle  of 
the  wire  as  possible.  If  it  is  kept  at  the  exact  middle,  the 
resistance  of  the  box  is  a  measure  of  the  unknown  resist- 
ance. It  is  readily  seen  that  for  accurate  measurements 
a  sensitive  galvanometer  must  be  employed,  since  the 
potential  difference  between  N  and  K  is  never  large. 
The  most  sensitive  arrangement  of  the  bridge  is  when 
the  resistances  of  the  four  arms  are  equal.  As  the  accu- 
racy of  the  method  depends  upon  the  uniform  resistance 
of  the  bridge  wire,  great  care  should  be  exercised  in 
making  contact  with  the  key  K,  not  to  press  it  down  so 
hard  as  to  bend  the  wire. 

The  Wheatstone  bridge  is  an  accurate  instrument  when 
understood  and  properly  used.  The  student  should  make 
numerous  measurements  with  it,  as  in  no  other  way  can 
its  capabilities  and  limitations  be  discovered. 

63.  The  Portable  Testing  Set  —  A  design  of  Wheatstone 
bridge  in  which  the  parts  of  the  bridge  wire  are  replaced 
by  plug  resistance  boxes,  and  which  also  contains  a  bat- 
tery, galvanometer,  and  rheostat  in  a  convenient  carrying 
case,  is  known  as  a  Portable  Testing  Set. 

It  is  capable  of  a  wide  range  of  measurements  and  is 
accurate  for  practical  purposes. 

The  connection  of  the  several  resistance  boxes  to  the 
battery  and  galvanometer  is  made  through  a  part  of  the 


DIVISION 

THE  PORTABLE   TESTING   SET 


71 


apparatus  called  the  commutator.  This  consists  of  four 
heavy  brass  blocks  that  serve  as  connections  to  the  arms 
of  the  bridge,  A  and  2?,  the  known  resistance  R,  and  the 
unknown  resistance  -X". 

Figure  68  shows  diagrammatically  the  connections,  from 
which  it  may  be  seen  that  the  function  of  the  commutator 
is  to  reverse  the  relative  positions  of  R  and  X  with  respect 


FIG.  68 


to  A  and  B,  the  arms  of  the  bridge.  When  the  resistance 
to  be  measured  is  high,  the  commutator  plugs  are  placed 
as  in  Fig.  68,  connecting  A  with  R  and  B  with  X,  in 


7} 

which   case   A  :  B  =  R  :  X,   and   X  =  —  R. 

A 


If   a   small 


resistance  is  to  be  measured,  the  plugs  are  placed  in  the 
other  diagonal,  connecting  A  with  X  and  B  with  R.     In 

this  case  A  :  B  =  X :  R,  and  X=  ^.R. 

Jj 

The  bridge  boxes  A  and  B  have  each  three  resistance 
coils,  of  1, 10,  and  100  ohms,  and  of  10, 100,  and  1000  ohms, 


72  ELECTRICITY 

respectively ;  hence  the  value  of  X  is  always  obtained  by 
multiplying  the  value  of  R  by  some  power  of  10. 

In  using  any  particular  testing  set,  certain  directions  for 
the  method  of  procedure  are  furnished  by  the  maker,  together 
with  the  values  of  resistances  in  the  bridge  and  rheostats 
that  should  be  used  to  secure  the  greatest  accuracy. 

In  general,  the  procedure  is  to  plug  the  commutator 
connection  in  the  diagonal  H  or  X,  depending  upon  the 
estimate  of  the  resistance  of  X  as  high  or  low,  unplug  the 
100-ohm  coil  in  each  of  the  bridge  arms  A  and  5,  and 
then  unplug  resistances  in  the  rheostat  until  its  total 
resistance  is  equal  to  the  estimate  of  the  resistance  of  X. 

Hold  the  batter}*-  key  down,  then  press  the  galvanometer 
key,  and  from  the  movement  of  the  needle  determine 
whether  the  resistance  in  the  rheostat  is  too  great  or  too 
small.  When  a  balance  has  been  obtained,  greater  accuracy 
should  be  secured  by  including  all  the  cells  of  the  battery 
and  making  the  ratio  of  the  resistances  in  A  and  B  such 
as  is  given  in  the  table  furnished  with  the  instrument. 

64.  The  Measurement  of  Resistance ;  Differential  Gal- 
vanometer Method.  —  Resistances  can  be  measured  by  the 
use  of  a  differential  galvanometer  as  follows  : 

EXPERIMENT  54.  —  To  measure  a  resistance  with  the  differential 

galvanometer. 

Apparatus.  —  A  differential 
galvanometer ;  resistance  box ; 
cells;  switch  ;  and  the  coil  to 
be  tested. 

Manipulation.  —  Couple  the 
apparatus  as  shown  in  Fig.  69, 
and  regulate  the  resistance  of 

FJG  6Q  the  box  until  there  is  no  deflec- 

tion of  the  needle.    When  this 
condition  is  secured,  the  reading  of  the  box  is  the  resistance  of  the  coil. 


THE  RESISTANCE  OF  PARALLEL   CIRCUITS         73 

As  this  is  a  nil  method,  it  is  better  adapted  to  the 
measurement  of  non-inductive  than  of  inductive  resist- 
ances. If  inductive  resistances  are  to  be  measured, 
the  current  must  be  allowed  to  flow  until  there  is  a 
steady  current  in  order  to  overcome  the  influence  of  the 
self-induction. 

65.  The  Resistance  of  Parallel  Circuits.  —  When  two 
points,  as  A  and  B  (Fig.  70),  are  connected  by  two  con- 
ductors, the  proportion 

of  the  total  current  that  1  I 

will  pass  through  each 
will    depend    upon    its  FlG>  70 

resistance.  If  these  resistances  are  equal,  the  currents 
will  be  equal,  and  each  will  be  one  half  the  total  current. 
If,  however,  the  resistances  are  unequal,  the  current  in 
each  will  be  proportional  to  the  resistance  in  the  other. 
This  may  be  expressed  by  the  proportion  0' :  C"  =  R" :  R', 
in  which  C'  and  R1  are  the  current  and  resistance  of  X, 
and  C"  and  R"  are  the  current  and  resistance  of  Y.  Since 
the  potential  difference  between  A  and  B  is  the  same  in 
both  wires,  the  respective  currents,  may  be  expressed  by 
the  equations 

<,_2 -a  a-.", 

ro  .  ru>  _  n  ni .  n"  —  7?"  •  7?' 

-j^i  -  ^77'  °  -U.K. 

The  part  of  the  current  passing  through  X  will  be 
given  by  the  proportion  C' :  O  =  R'1 :  R1'  +  R1,  in  which 
C  is  the  total  current. 

The  combined  or  parallel  resistance  of  X  and  Y  is 
equal  to  the  product  of  the  resistances  divided  by  their 


74  ELECT1UCITY 

R'  R'f 

sum  ;  that  is,  Rp  =  —  -  —  •     For  when  the  electro-motive 
./t  -\-  .K 

force  is  1,  0'=—,  and  0"  =  -—  ;  therefore 

-it  All 

tf'  +  tf"=-l       1     =R'  +  R". 
R'     R"        R'R" 

and  since  C'  +  O"  =  (7,  the  whole  current,  hence  0=R  ^"^   ; 

1  R1  Rff 

and  since  Rp——,  therefore  Rp  =  —  -  —  -• 

C  £l>    -j-   /t 

For  example,  if  R'  =  3  ohms  and  J?"  =  5  ohms,  then 


For  more  than  two  branches,  three  for  example,  the  value 
•ill  1  R'R'R" 

_1_      J_     J_  "  ^'^"  +  .B'  JK";  +  #"72"'  ' 
#'      #"      #'" 

This  may  be  stated  as  follows  :  The  parallel  resistance  of 
several  circuits  may  be  obtained  by  dividing  the  product 
of  all  the  resistances  by  the  sum  of  the  products  of  each 
resistance  by  all  the  others  taken  separately  ;  or  it  is  the 
reciprocal  of  the  sum  of  the  reciprocals  of  all  the  resistances 
taken  separately. 

EXPERIMENT  55.  —  To  measure  the  parallel  resistance  of  lamps. 

Apparatus.  —  A  lamp  board  with  a  half  dozen  lamp  bases  and 

binding  posts  as  shown  in  the 
figure;  a  half  dozen  lamps  of 
different  candle  power. 

Ma  nipulation.  —  Measure 


the  resistance  of  each  lamp 
separately.  Measure  the  resistance  of  the  lamps  in  parallel  in  groups 
of  two  at  a  time,  then  in  groups  of  three  at  a  time,  and  so  on.  Com- 
pare the  measured  resistances  with  those  obtained  by  substituting 
the  separate  resistances  in  the  above  formula. 


SHUNTS  75 

The  results  of  this  experiment  should  show  agreement  within  nar- 
row limits.  The  parallel  resistance  of  two  conductors  is  always  less 
than  the  resistance  of  either  taken  alone. 

66.  Shunts.  —  The  principle  of  divided  or  parallel  cir- 
cuits is  applicable  in  the  case  of  shunts.  If  it  is  desired 
to  measure  a  current  greater  than  can  be  measured  by  the 
galvanometer  or  ammeter,  a  part  of  the  current  can  be 
sent  through  a  resistance  in  parallel  with  the  instrument, 
and  this  is  called  a  shunt. 

The  parallel  coupling  of  a 
galvanometer  and  its  shunt  is 
shown  in  Fig.  72. 

The  ratio  of  the  currents  in 
the  two  circuits  will  be  expressed 
by  the  proportion  Off:Os  =  Rs:  Rg, 
while  the  ratio  of  the  galvanom- 
eter current  to  the  total  current  will  be  Cg :  C  =  Rs:Rg 

A  convenient  arrangement  is  to  have  the  current  in  the 
galvanometer  one  tenth  of  the  whole  current;  then  the 
resistance  of  the  shunt  will  be  one  tenth  of  the  sum  of 
the  two.  In  this  case,  Rs :  Rg  +  Rs  =  1 :  10,  hence 

Rq  +  Rs=  10 Rs,  and  9 Rs  =  Rg,  or  Rs  =  £  Rg. 
This  is  what  is  called  a  tenth  shunt,  for  the  whole  current 
will  be  obtained  by  multiplying  the  galvanometer  current 
by  10.  -  In  the  same  way,  a  hundredth  shunt  can  be  shown 
to  be  one  in  which  Rs  =  ^  Rg. 

EXPERIMENT  56.  —  To  make  a  tenth  shunt  for  a  galvanometer. 

Apparatus.  —  A  low-reading  galvanometer,  and  a  spool  of  high- 
resistance  wire. 

Manipulation.  —  Measure  the  resistance  of  the  galvanometer.  Cut 
from  the  spool  of  wire  a  piece  10  ft.  long  and  measure  its  resist- 
ance. Compute  the  length  of  wire  required  to  make  a  tenth  shunt. 
Cut  from  the  spool  a  piece  2  ft.  longer  than  the  computation  calls 


76 


ELECTRICITY 


for.  Measure  its  resistance  and  reduce  the  length  of  the  wire, 
measuring  the  resistance  each  time,  until  the  exact  length  is  found. 
Wind  this  wire  into  a  non-inductive  resistance  coil  by  winding  it  on 
a  spool  double,  beginning  at  the  middle.  This  method  of  winding  is 
a  convenient  one,  since  it  brings  both  ends  of  the  coil  on  the  outside. 
In  order  to  verify  the  accuracy  of  the  work,  it  will  be  well  to 
compare  the  readings  of  the  shunted  galvanometer  with  those  of 
a  reliable  ammeter.  What  change  has  been  made  in  the  usefulness 
of  the  galvanometer  ? 


67.  The  Internal  Resistance  of  Batteries.  —  The  fact 
that  a  battery  is  a  generator  makes  it  more  difficult  to 
measure  its  resistance  than  it  is  to  measure  the  resistance 
of  a  coil  of  wire.  The  following  are  some  of  the  methods 
used : 

EXPERIMENT  57.  —  (a)  The  three-cell  method. 

Apparatus.  —  Three  cells,  two  of  which  have  the  same  electro- 
motive force  ;  the  substitution  board  used  in  Experiment  50 ;  a  resist- 
ance box ;  and  a  galvanometer. 

Manipulation.  —  Consider  the  cell  A  (Fig.  73)  as  the  source  of 

E.  M.  F.,  while  the  two  equal 
cells  B  and  C  are  coupled  so  as 
to  oppose  each  other.  Connect 
these  cells  and  the  resistance 
box  as  in  the  substitution 
method  of  measuring  resist- 
ance, and  find  their  resistance. 
The  method  will  not  be 
accurate  unless  the'  cells  C 
and  B,  when  coupled  as  in  the 
figure,  give  no  current.  It  is 
not  a  method  that  can  be  relied 
upon  for  the  greatest  accuracy 
under  any  circumstances. 

EXPERIMENT  58.  —  (ft)  Mance's  method. 

Apparatus.  —  The  cell,  the  resistance  of  which  is  to  be  measured;  a 
Wheatstone  bridge ;  connecting  wires ;  and  a  contact  key. 


THE  INTERNAL  RESISTANCE  OF  BATTERIES      77 


Manipulation.  —  Place  the  cell  in  one  of  the  arms  of  the  bridge,  as 
shown,  and  place  the  key  between  A  and  D  instead  of  in  the  galva- 
nometer circuit  BC.  Vary  the 
resistance  of  the  box  until  such 
a  resistance  is  found  that  the 
opening  and  closing  of  the 
key  makes  no  difference  in 
the  deflection  of  the  galva-  A 
nometer.  When  such  a  resist- 
ance is  found,  it  is  equal  to 
the  resistance  of  the  cell,  pro- 
vided that  AB  is  one  half  of 
AD.  This  is  a  satisfactory 

method  except  that  it  requires  a  different  form  of  coupling  for  the 
bridge,  and  takes  considerable  time  to  complete. 


EXPERIMENT  59.  —  (c)  The  voltmeter  method. 
Apparatus.  —  A  low-reading  voltmeter;  ammeter;  resistance  box; 
a  two-way  switch;   and  the  cell  the  resistance  of  which  is   to   be 
measured. 

Manipulation.  —  Couple  the  apparatus  as  in  the  figure  and  take  the 
reading  of  the  voltmeter.  Throw  the  switch  from  the  voltmeter  to 

the  ammeter  circuit  and  take 
the  reading  of  the  ammeter 
as  soon  as  possible.  Substi- 
tute these  readings  in  the 

E 

expression    R  =  —  and  find 

C 

the  value  of  R.  This  gives 
the  resistance  of  the  ammeter 
circuit.  Subtract  the  resist- 
A  ance  of  the  ammeter,  resist- 
ance box,  leading  wires,  and 
switch,  and  the  remainder 
gives  the  resistance  of  the  cell. 

This  method  assumes  that  the  difference  of  potential  at  the  ter- 
minals of  the  cell,  measured  by  the  voltmeter,  is  the  E.  M.  F.  of  the 
cell.  With  a  voltmeter  that  can  be  read  to  the  hundredth  of  a  volt 
it  is  a  rapid  and  accurate  method. 


FIG.  75 


78  ELECTRICITY 

EXPERIMENT  60.  —  (d)  A  modification  of  (c). 

Apparatus.  —  The  cell,  resistance  box,  and  the  voltmeter  used  in 
Experiment  59;  and  two  switches. 

Manipulation.  —  Couple  the  apparatus  so  that  the  voltmeter  may 
be  thrown  into  the  circuit  alone  or  in  parallel  with  the  resistance 
box.  Throw  the  voltmeter  into  the  circuit  and  call  the  reading  V- 
Throw  the  resistance  in,  in  parallel  with  the  voltmeter,  and  take  a 
second  reading  immediately  after  the  drop  that  takes  place  on  throw- 
ing the  switch.  Call  this  reading  V".  Measure  the  resistance  of  the 
switch  and  connecting  wires,  add  this  to  the  reading  of  the  resistance 
box,  and  call  it  R'.  Then  C  =  ~  Call  the  resistance  of  the  cell 

\rr         T///  f* 

R.     Then  R  =  l         v    . 

C 

NOTE.  —  When  the  voltmeter  switch  is  closed,  the  reading  must  be 
taken  immediately  on  account  of  the  polarization  of  the  cell.  The 
effect  of  this  polarization  will  be  shown  by  a  gradual  decrease  in  the 
reading. 

68.  Variation  of  Resistance  with  Temperature.  —  Makers 
of  resistance  boxes  to  be  used  where  a  high  degree  of 
accuracy  is  necessary  always  state  the  temperature  at 
which  the  box  will  give  the  rated  resistance,  as  well  as  the 
temperature  coefficient.  In  order  to  determine  this  varia- 
tion some  method  of  taking  the  resistance  at  different 
temperatures  must  be  used. 

EXPERIMENT  61.  —  To  determine  the  temperature  coefficient. 

Apparatus.  —  (a)  German  silver.  A  coil  of  fine  German  silver  wire  ; 
a  number  of  battery  cells;  a -thermometer ;  beaker;  and  a  Bunsen 
burner. 

Manipulation.  —  Fill  the  beaker  with  cold  water  and  take  its  tem- 
perature. Insert  the  coil  in  the  beaker  and  measure  its  resistance. 
Heat  the  water  to  a  temperature  of  60°  and  again  measure  the  resist- 
ance of  the  coil.  Bring  the  water  to  the  boiling  point  and  measure 
again. 

From  the  results  obtained  determine  the  temperature  coefficient, 
i.e.  the  change  of  the  resistance  per  degree  of  temperature,  for  German 
silver.  The  determination  of  this  coefficient  is  important,  since- the  use 
of  a  large  current  heats  a  conductor  and  hence  changes  its  resistance. 


VARIATION   OF  RESISTANCE    WITH   TEMPERATURE     79 

(b)  Copper.  Repeat  the  experiment  with  a  copper  wire  of  the 
same  resistance. 

EXPERIMENT  62.  —  The  effect  of  raising  the  temperature  of  carbon, 
upon  its  resistance. 

Apparatus.  —  A  small  carbon  pencil,  such  as  is  sometimes  used  in 
projection  lanterns ;  a  number  of  storage  cells,  or  a  dynamo  ;  ammeter, 
voltmeter,  and  Wheatstone  bridge. 

Manipulation.  —  Measure  the  cold  resistance  of  the  carbon  by  the 
Wheatstone  bridge  method.  Send  enough  current  through  the  pencil 
to  raise  it  to  a  high  temperature,  and  measure  the  resistance  by  the 
fall  of  potential  method. 

How  does  carbon  compare  with  German  silver  in  regard  to  the 
relation  between  temperature  and  resistance?  How  does  it  compare 
with  copper  ? 

EXPERIMENT  63.  —  To  compare  the  hot  resistance  of  incandescent 
lamps  with  their  resistance  when  cold. 

Apparatus.  —  Dynamo  or  storage  cells;  incandescent  lamps  of  the 
proper  voltage  for  the  circuits  used ;  ammeter ;  voltmeter ;  and 
Wheatstone  bridge. 

Manipulation. — Measure  the  cold  resistance  of  one,  five,  and  ten  lamps 
by  the  Wheatstone  bridge.  Bring  the  lamps  up  to  their  proper  voltage 
and  measure  their  hot  resistance  by  the  fall  of  potential  method. 

Compare  the  results  of  these  experiments  and  state  the  importance 
of  these  results. 

EXPERIMENT  64.  —  To  measure  the  resistance  of  an  arc  light. 

Apparatus.  —  A  dynamo;  hand-regulated  arc  lamp ;  ammeter;  and 
voltmeter. 

Manipulation.  —  («)  Run  the  lamp  with  a  nine,  a  ten,  and  a  twelve 
ampere  current,  keeping  the  distance  between  the  carbon  points  con- 
stant, and  not  over  a  quarter  of  an  inch.  Measure  the  resistance  for 
each  by  the  fall  of  potential  method. 

(b)  Repeat  the  measurements  with  a  long  arc,  keeping  the  length 
constant. 

(c)  Start  the  lamp  with  a  short  arc  and  let  it  burn  until  the  arc 
breaks.    Measure  the  resistance  at  different  times.     Measure  the  final 
length  of  the  arc  and  determine  the  rate  of  consumption  of  the  carbons. 
How  does  the  resistance  of  the  arc  vary  with  its  length?     Does  its 
resistance  vary  with  the  current  used? 


80 


ELECTRICITY 


69.  Insulation  Resistance.  —  It  is  frequently  necessary 
to  have  a  rapid  method  of  finding  the  resistance  of  a 
certain  insulation.  The  following  method  fulfills  the 
requirements. 

EXPERIMENT  65.  —  To  measure  insulation  resistance  with  volt- 
meters. 

Apparatus.  —  Two  high-resistance  voltmeters;  a  dynamo  or  storage 
battery;  and  the  insulation  to  be  measured. 

Manipulation.  —  Let  the  points  A  and  B  be  the  terminals  of  the 
electric  generator.  Couple  one  voltmeter  directly  to  these  terminals. 

Couple  one  binding  post 
of  the  other  voltmeter  to 
one  of  these  terminals,  as 
A,  and  the  other  to  one 

Oside  of  the  insulation. 
B  Couple  B  to  the  other  side 
of  the  insulation  and  take 
simultaneous  readings  of 
the  two  voltmeters. 

Let  V  represent  the 
reading  of  the  first  volt- 
meter, V"  that  of  the 
second,  r  the  resistance 
of  the  second  voltmeter, 
and  R  the  resistance  of 
Hence  S 


FIG.  76 


the  insulation  ;    then  V"  :  V  -  V"  =  r  :  R. 


70.  The  Resistance  of  Electrolytes.  —  An  electrolyte  is 
any  solution  that  is  a  conductor  for  an  electric  current. 
When  a  current  passes  through  such  a  conductor,  a  decom- 
position, called  electrolysis,  takes  place  in  the  solution.  The 
plate  by  which  the  current  enters  the  solution  is  called 
the  positive  electrode,  or  anode,  and  that  by  which  the  cur- 
rent leaves  the  solution  is  called  the  negative  electrode, 


THE  RESISTANCE  OF  ELECTROLYTES 


81 


or  cathode.  The  determination  of  the  resistance  of  an 
electrolyte  is  complicated  by  the  counter  electro-motive 
force  that  is  set  up  whenever  a  current  is  sent  through  it. 
This  difficulty  is  overcome  in  the  following  method : 


EXPERIMENT  66.  —  To  measure  the  resistance  of  an  electrolyte. 

Apparatus.  —  A  glass  tube  an  inch  in  diameter  and  a  foot  long; 
two  pieces  of  platinum  wire  6  in.  long;  cells;  a  galvanometer;  resist- 
ance box ;  switch  ;  and  a  solution  of  copper  sulphate. 

Manipulation.  —  Wind  each  platinum  wire  into  a  flat  spiral  that 
will  nearly  fill  the  tube.  Close  the  end  of  the  tube  in  a  Bunsen  flame, 
sealing  in  one  of  the  platinum  spirals  as  shown.  Solder  the  other 
spiral  to  an  insulated  copper  wire  and  paraffin  the  latter  for  a  foot 
from  the  joint.  Couple  the  apparatus  as 
shown  in  Fig.  77,  and  send  a  current  through 
the  circuit  when  the  upper  spiral  is  in  the 
position  P',  regulating  the  resistance  in  the 
box  until  a  suitable  deflection  is  obtained  in 
the  galvanometer.  Lower  the  upper  spiral 
to  a  second  position  P",  sending  a  current 
through  the  circuit  a  second  time,  changing 
the  resistance  in  the  box  until  the  deflection 
of  the  galvanometer  is  the  same  as  before. 
When  this  condition  is  secured,  the  resistance 
added  in  the  box  will  be  the  resistance  of  the 
liquid  column  P'P".  Since  this  measurement 
gives  the  resistance  of  the  column  P'P",  the 
resistance  of  the  column  per  unit  length  is  readily  found.  It  is  well 
in  every  measurement  to  leave  the  current  on  only  long  enough  to 
take  the  readings.  Notes  should  be  made  of  the  per  cent  of  the 
solution  and  of  the  temperature  at  the  time  of  the  experiment,  as 
both  of  these  conditions  modify  the  results. 

EXPERIMENT  67.  —  To  measure  the  resistance  of  an  electrolyte 
with  the  alternating  current. 

Apparatus. — The  electrolytic  tube  used  in  Experiment  66;  a 
Wheatstone  bridge;  resistance  box;  induction  coil;  telephone  re- 
ceiver; and  cells. 

ELEC.   AND  MAG.  — 6 


FIG.  77 


82 


ELECTRICITY 


Manipulation.  —  Couple  the  apparatus  as  in  Fig.  78,  placing  the 
induction  coil  at  such  a  distance  (in  another  room  if  necessary)  that 
the  noise  of  the  contact  breaker  can  not  be  heard.  Find  by  trial  a 
point  D  in  the  bridge  wire  that  will  give  the  least  sound  in  the  receiver. 


C 


I        1 

o  o  o  o 

1 

0              0 

1 

0              0 

-hi 

0              0 

19 

?         9 

xL 

1     1 

L 

i      ib                 (. 

1                             Ol          IO 

J 

J 


FIG.  78 

When  this  point  is  determined,  the  resistance  may  be  computed  by 
applying  the  law  of  the  bridge. 

If  the  point  D  is  in  the  middle  of  the  bridge  wire,  the  resistance  of 
the  electrolyte  is  the  same  as  that  in  the  box. 

71.  The  Unit  of  Resistance,  the  Ohm.  —  Mention  has 
been  made,  in  Section  37,  of  the  ohm  as  the  unit  of  elec- 
trical resistance.  The  unit  in  use  at  the  present  time 
is  the  international  ohm.  This  was  recommended  at  the 
meeting  of  the  British  Association  in  1892,  was  adopted 
by  the  International  Electrical  Congress  held  in  Chicago 
in  1893,  and  was  legalized  for  use  in  the  United  States 
by  Act  of  Congress  in  1894. 

It  is  defined  as  the  resistance  of  14.4521  g.  of  mercury  in 
the  form  of  a  column  of  uniform  cross  section,  106.3cm.  in 
length,  at  a  temperature  of  0°  C.  This  is  equivalent  to  a 


THE   UNIT   OF  RESISTANCE  83 

column  106.3  cm.  long,  having  a  uniform  cross  section  of 
1  sq.  mm.  Previous  to  this  there  had  been  three  more 
or  less  generally  accepted  values  of  the  ohm. 

First :  The  Siemens  Unit.  This  was  the  resistance  of 
a  column  of  mercury  100  cm.  long  and  1  sq.  mm.  in  cross 
section,  at  0°  C. 

Second :  The  B.  A.  (British  Association)  Unit.  In  this 
the  mercury  column  was  1  sq.  mm.  in  cross  section  and 
approximately  104.9  cm.  long. 

Third:  The  unit  adopted  by  the  Paris  Conference  of 
1884,  which  was  defined  in  the  same  terms,  except  that 
the  length  was  given  as  106  cm.  This  was  called  the 
Legal  Ohm. 

The  comparative  values  of  these  units  are  as  follows : 


UNIT 

VALUE 

DATE 

International  Ohm    

1.000 

1893 

Legal  Ohm      

9972 

1884 

B.  A.  Ohm  ......          .     . 

9866 

1864 

Siemens  Unit 

9407 

72.  Rheostats.  —  A  rheostat  is  a  device  for  regulating 
the  resistance  in  an  electric  circuit.  There  are  many  forms, 
that  vary  with  the  requirements  of  the  circuit  in  which 
they  are  used.  Examples  of  the  most  useful  types  are  as 
follows : 

(a)   The  Lamp  Resistance  Board. 

A  serviceable  rheostat  can  be  made  by  fixing  a  number  of 
lamp  bases  to  a  board  and  connecting  them  in  parallel 
between  the  wires  that  lead  out  from  two  binding  posts. 
Figure  79  shows  a  form  of  high-resistance  lamp  made 
especially  for  this  use.  Lamps  that  have  been  in  use  so 


84 


ELECTRICITY 


long  that  they  are  practically  useless  for  lighting  purposes 
are  still  of  use  as  resistances  in  a  board  of  this  kind. 


FIG.  80 


FIG.  79 

(£)   The   Coiled   Wire  Rheostat. 

The  principle  of  this  rheostat  is  shown  in  Fig.  80.  Jt 
consists  of  a  coil  of  uncovered  resistance  wire  wound 
spirally  on  an  insulated  cylinder  AB  that  is  supported 

at  the  ends.  One  end  of 
the  coil  is  fastened  to  a 
binding  post  on  the  base 
of  the  support  at  E,  and 
the  other  end  to  a  sliding 
contact  H  which  is  con- 
nected to  the  binding  post  at  F.  This  contact  can  be 
moved  to  any  position  along  the  rod  (7J9,  the  part  of  the 
coil  in  the  circuit  being  only  that  between  the  end  E  and 
the  sliding  contact  H. 

(c)   The  Ironclad  Rheostat. 

One  of  the  commercial  forms  of  this  rheostat  is  shown 
in  Fig.  81.  It  consists  of  an  iron  plate,  over  the  face  of 
which  moves  a  brass  arm  (7Z>,  pivoted  at  C.  The  end  D 
of  this  arm  makes  electrical  contact  with  the  ends  of 
brass  plugs  that  pass  through  the  iron  plate  and  are  in- 
sulated from  it.  The  resistances  are  made  of  thin  strips 


RHEOSTATS 


85 


of  iron  bent  back  and  forth  upon  themselves.     These  are 

upon  the  back  side  of  the  plate  and 

are  connected  to  the  brass  plugs  as 

shown.    The  binding  post  A  is  con- 

nected to  the  brass  arm  at  (7,  while 

the    second    binding    post    is    con- 

nected   directly   to   the   last   plug. 

Tracing    the   path   of   the   current 

will  show  the  part  of  the  resistance 

that  is  in  use  with  any  position  of 

the  arm.  FlG  81 

EXPERIMENT  68.  —  The  study  of  a  rheostat. 

Apparatus.  —  An  ironclad  rheostat  with  from  20  to  40  plugs;  appa- 
ratus for  the  measurement  of  its  resistance. 

Manipulation.  —  Measure  the  resistance  of  the  rheostat  with  the  arm 
resting  on  each  plug  in  turn. 

Make  a  curve  of  the  resistance,  laying  off  resistances  along  the  verti- 
cal axis  and  the  number  of  sections  along  the  horizontal. 


The   Water  Rheostat. 
A  resistance  that  can  carry  a  heavy  current  and  that 
allows  a  rapid  adjustment  is  frequently  needed  in  prac- 
tical work. 

Figure  82  shows  a  simple  form  of 
rheostat  that  meets  the  requirement. 
A  barrel  or  keg  is  fitted  with  a  cover 
through  the  middle  of  which  passes  a 
rod  carrying  an  iron  plate  A.  This 
rod  can  be  clamped  in  any  position  and 
FlG>  82  is  fitted  with  a  binding  post.  A  second 

iron  plate  is  connected,  by  means  of  a  heavy  rubber-covered 
wire,  with  the  binding  post  C.  The  solution  is  usually 
water  to  which  a  small  quantity  of  salt  has  been  added. 


86  ELECTRICITY 

This  form  of  rheostat  is  sometimes  called  an  "  absorption 
rheostat,"  since  it  is  frequently  used  in  testing  a  dynamo, 
in  which  case  the  current  is  not  put  to  any  useful  purpose. 

(e)  The  Mercury  Rheostat. 

This  device  is  adapted  to  the  case  which  requires  a  small 
resistance  that  can  be  changed  a  very  little  at  a  time. 
A  row  of  holes  are  bored  along  each  of  two  opposite 
sides  of  a  well-seasoned  oak  plank.  These  are  connected 
by  channels  cut  out  of  the  plank,  as  xy.  An  elevated 
edge  is  then  put  around  the  board,  and  it  is  thoroughly 

paraffined  arid  placed  upon 
a  level  support.  Mercury  is 
then  poured  into  the  channels 


(a) 


J/9 


JL 


to  any  desired  depth,  and 
they  are  connected  by  a  series 
of  copper  straps  shaped  as 
in  figure  (a).  By  coupling 
the  board  into  the  circuit  by 
FlG  83  ~B  '  the  binding  posts  A  and  B, 

any  resistance  from  a  maxi- 
mum to  a  short  circuit  can  be  obtained  by  the  proper 
arrangement  of  the  connecting  straps. 

QUESTIONS  AND  PROBLEMS 

1.  If  L  in  the  formula  for  the  resistance  of  a  wire,  Section  56,  is  in 
feet,  and  D  in  thousandths  of  an  inch,  the  value  of  k  for  copper  is  10.39. 
Find  the  resistance  of  a  spool  containing  100  ft.  of  No.  30  copper  wire. 

2.  What  is  the  resistance  of  a  spool  of  100  ft.  of  No.  30  German 
silver  wire,  if  the  value  of  k  for  German  silver  is  136.00? 

3.  On  sending  a  current  of  25  amperes  through  a  copper  strap,  the 
difference  of  potential  at  its  ends  was  found  to  be  1.82  volts.     What 
was  the  resistance  of  the  strap  ? 

4.  Three  wires  having  resistances  of  3,  6,  and  9  ohms  respectively 
are  coupled  in  parallel.     What  is  their  combined  resistance? 


THE   UNIT  OF  CURRENT  87 

5.  What  must  be  the  resistance  of  a  tenth  shunt  of  a  galvanom- 
eter, the  resistance  of  which  is  40  ohms?     What  must  it  be  for  a 
fifth  shunt? 

6.  A  voltmeter  coupled  to  the  terminals  of  five  cells  in  series 
reads  6.86  volts.     On  sending  the  current  from  the  cells  through  a 
resistance  of  5  ohms,  the  voltmeter  reading  drops  to  3.8.     Find  the 
resistance  per  cell. 

7.  Devise  a  lamp  board  that  will  give  a  wide  range  of  resistances, 
and  state  some  of  the  advantages  of  such  a  resistance  board. 

8.  What  is  the  practical  value  of  the  difference  between  the  cold 
and  the  hot  resistance  of  incandescent  lamps? 

9.  An  inclosed  arc  lamp  requires  a  current  of  4.5  amperes  when 
on  a  110-volt  circuit.     What  is  the  resistance  of  the  lamp?     The  fall 
of  potential  across  the  arc  is  80  volts.     What  is  the  resistance  of  the 
coil  in  series  with  it? 

10.  If  a  voltmeter,  the  resistance  of  which  is  20,000  ohms,  is  put 
in  series  with  an  insulation  resistance  on  a  110-volt  circuit  and  gives 
a  reading  of  6.52  volts,  what  is  the  resistance  of  the  insulation? 
What  resistance  will  give  a  reading  of  1.42  volts? 

11.  A   certain   resistance   was    measured    in    1890   as  236   ohms, 
using  a   resistance   box   made   in    1870.      What   was   its   resistance 
in  legal  ohms?     What  would  it  be  in  international  ohms  if  measured 
to-day? 

CURRENT,  ETC. 

73.  The  Unit  of  Current ;  the  Ampere.  —  The  electric 
current  can  be  measured  by  its  magnetic  effect,  or  by  its 
chemical  effect,  or  by  its  heating  effect.  As  a  matter  of 
fact,  the  unit  of  current  is  defined  and  measured  by  the 
chemical  effect,  while  most  of  the  practical  measuring 
instruments  make  use  of  the  magnetic  effect. 

The  unit  of  current  is  the  international  ampere.  This 
is  a  current  of  unvarying  strength  that  will  deposit 
.001118  g.  (.01725  grain)  of  silver  per  second  from  a 
certain  solution  of  silver  nitrate.  The  same  current  will 
deposit  .00032959  g.  (.005086  gram)  of  copper  per  second 
from  a  certain  solution  of  copper  sulphate. 


88 


ELECTRICITY 


74.  The  Measurement  of  Current ;  the  Electrolytic  Method. 

—  EXPERIMENT  69.  —  To  measure  a  current  by  the  copper  voltameter. 
Apparatus.  —  A  copper  voltameter;   galvanometer;   cells;  switch; 
a  mercury  rheostat ;  and  a  timepiece. 

Manipulation.  —  Make  the  copper  sulphate  solution  by  dissolving 
crystals  of  copper  sulphate  in  distilled  water  to  which  one  per  cent  of 
sulphuric  acid  has  been  added.  The  density  of  the  solution  should 
be  about  1.15.  Place  this  solution  in  a  large  beaker  or  battery  jar,  and 
for  electrodes  use  either  flat  coils  of  uncovered  copper  wire  or  copper 
plates.  These  must  be  thoroughly  cleaned  and  washed  before  use. 

If  plates  are  used,  the  cathode 
upon  which  the  copper  will 
be  deposited  should  be  of  thin 
copper,  so  that  any  increase  in 
its  weight  can  be  more  accu- 
rately determined.  After  the 
plates  have  been  weighed  the 
apparatus  should  be  coupled  in 
series,  and  the  time  noted  when 

the  current  is  turned  on.  Keep  the  current  constant  by  regulating 
the  rheostat  so  that  the  reading  of  the  galvanometer  shall  be  uni- 
form, and  take  the  time  when  the  current  is  turned  off.  Wash  and 
dry  the  cathode  thoroughly  and  weigh  it. 

From  the  difference  in  the  weight  of  the  cathode  before  and  after 
the  experiment  determine  the  current  used.  Does  this  experiment 
suggest  a  method  of  calibrating  the  galvanometer,  i.e.  determining  the 
galvanometer  constant? 

75.  The  Measurement  of  Current ;  the  Fall  of  Potential 
Method. —  In  order  to  apply  the  fall  of  potential  method  to 
the  measurement  of  the  current,  it  is  necessary  to  have  a 
known  resistance  that  will  not  change  in  amount  on  hav- 
ing a  current  sent  through  it.      This  method   makes   it 
possible  to  use  any  low-reading  voltmeter  as  a  direct-read- 
ing ammeter  for  small  currents. 

EXPERIMENT  70.  —  To  measure  a  current  by  the  fall  of  potential 
method. 


THE   UNIT  OF  ELECTRO-MOTIVE  FORCE 


89 


Apparatus.  —  Large  size  resistance  wire ;  a  direct-reading  voltmeter 
giving  full  scale  deflection  for  five  or  ten  volts ;  an  ammeter ;  rheostat ; 
cells  ;  and  a  switch. 

Manipulation. —  Cut  from  the  resistance  wire  a  sufficient  length  to 
measure  one  tenth  of  an  ohm,  and  wind  it  into  a  non-inductive  coil  of 
large  diameter.  Couple  this  coil  in  series  with  the  cells,  rheostat, 
switch,  and  ammeter.  Couple  the  voltmeter  as  a  shunt  to  the  coil  and 
send  a  current  through  the  circuit.  Take  simultaneous  readings  of 
the  voltmeter  and  ammeter  and  compare  the  results.  Send  a  number 
of  different  currents  through  the  circuit,  regulating  the  amount  of 
current  by  the  rheostat,  and  find  whether  the  accuracy  of  the  voltmeter 
readings  is  affected  by  the  change  of  the  temperature  of  the  coil  due 
to  the  heating  effect  of  the  larger  currents  sent  through  it. 

A  study  of  this  kind  will  show  the  limitations  of  the  method  and 
the  necessity  of  having  a  small  resistance  in  the  coil  and  a  low-reading 
voltmeter.  A  resistance  wire  with  a  small  temperature  coefficient  will 
give  the  most  satisfactory  results. 

An  accurate  form  of  ammeter  is  made  on  this  principle. 
The  coil,  or  shunt  box,  is  of  very  small  resistance,  and  in- 
stead of  a  voltmeter  .._,._ 
a  millivoltmeter  is 
used.  The  shunt  box 
is  frequently  arranged 
so  that  the  millivolt- 
meter  will  read  five 
amperes,  say,  for  the 
full  scale,  when  at- 
tached to  the  binding  posts  A  and  C,  and  fifty  amperes 
when  attached  to  A  and  B. 


LINE  WIRE 

13 

c 

ho 

LINE  WIRE               p 

6|    [5 

"1 

r 

VM 


FIG.  85 


76.   The  Unit  of  Electro-motive  Force ;  the  Volt.  —  The 

present  unit  of  electro-motive  force  is  the  international 
volt,  which  is  the  E.  M.  F.  that  steadily  applied  to  a  con- 
ductor, the  resistance  of  which  is  one  international  ohm, 
will  produce  a  current  of  one  international  ampere.  There 


90 


ELECTRICITY 


is  no  standard  cell  that  gives  an  E.M.F.  of  one  volt,  but 
the  Clark  cell,  at  a  temperature  of  15°  centigrade,  gives  a 
uniform  E.  M.  F.  of  1.434  volts,  and  is  taken  as  a  standard 
at  that  rating.  The  gravity  cell  gives  an  E.  M.  F.  of  nearly 
one  volt  and  makes  a  fairly  good  unit. 


77.  The  Measurement  of  Electro-motive  Force  ;  the  Poten- 
tiometer Method.  —  A  potentiometer  is,  in  principle,  a  high- 
resistance  wire  of  uniform  diameter  stretched  between  two 
binding  posts  in  such  a  way  that  contact  can  be  made  at 
its  ends  and  along  its  length.  The  wire  of  a  Wheatstone 
bridge  can  be  used  for  the  purpose. 

EXPERIMENT  71.  —  To  measure  the  E.  M.  F.  of  a  cell  with  a  poten- 
tiometer. 

Apparatus.  —  A  potentiometer;  gravity  cells;  switch;  galvanom- 
eter; voltmeter;  standard  cell;  and  the  cell  to  be  measured. 

Manipulation.  —  Couple  the  apparatus  as  in  the  figure.     Close  the 

switch  S  and  read  the 

^ fall  of  potential  from 

B  to  A.  Having  the 
switch  S  closed,  touch 
the  wire  with  the  key 
K,  and  find  such  a  posi- 
tion for  it  that  there 
will  be  no  deflection  of 
the  galvanometer  f7, 
in  series  with  the  stand- 
ard cell  E.  Read  the 
distance  AK  and  call 
it  Z',  the  distance  AB 
being  L.  Find  a  point  K'  such  that  the  cell  to  be  measured,  E',  will 
give  no  deflection  to  the  galvanometer,  and  call  the  distance  AK',  L". 
The  reading  of  the  voltmeter  will  give  the  fall  of  potential  from 
B  to  A,  and  since  the  galvanometer  shows  that  there  is  no  current 
when  the  key  is  depressed,  the  fall  of  potential  from  K  to  A  must  be 
the  same  as  the  E.  M.  F.  of  the  cell.  Hence  the  following  propor- 


G' 


E' 


G® 


E 


>*' 


1; 


FIG.  86 


ELECTRO-MOTIVE  FORCE  91 

tion  holds :   V:E  =  L:Lf.     The  E.  M.  F.  of  the  cell  E'  is  found  from 

(  L"\ 
the  proportion  E  :  E'  =  L' :  L",  from  which  E'  =  E(JT}' 

If  the  resistance  of  the  switch  S  and  the  connections  from  the 
battery  to  the  terminals  A  and  B  is  small,  the  potential  difference  of 
the  battery  =  V -=  E~- 

j  j 

78.  The  Measurement  of  Potential  Difference  by  Ohm's 
Law. — A  modification  of   the  fall   of  potential  method 
of  measuring  resistances  can  be  used  to  determine  the 
difference    of    potential   at    the   terminals    of    a    cell    as 
follows  : 

EXPERIMENT  72.  —  Ohm's  law  applied  to  the  measurement  of 
potential  difference. 

Apparatus.  —  A  coil  of  known  resistance;  an  ammeter;  cells;  and 
a  switch. 

Manipulation.  —  Couple   the   apparatus  as  in   Fig.  87.     Send  the 
current  through  the  circuit 
and  take   a  reading  of  the 
ammeter. 

The  product  obtained  by 
multiplying  the  sum  of  the 
resistances  of  the  coil  and 
ammeter  by  the  ammeter 
reading  will  give  the  fall  of 
potential  between  the  points 
B  and  C.  By  knowing  the 

resistances  of  the  connecting  wires  and  switch,  as  well  as  that  of  the 
ammeter  and  coil,  the  potential  difference  at  the  terminals  of  the 
battery  can  be  determined. 

79.  The  Calibration  of  Instruments.  —  Early  forms  of 
ammeters  and  voltmeters  were  made  with  the  scale  divided 
in  degrees,  so  that  it  became  necessary  to  calibrate  them 
in  order  to  know  the  value  of  a  given  deflection. 

This  was  sometimes  done  by  finding  the  reduction  fac- 
tor by  means  of  which  the  deflection  could  be  changed  to 


92 


ELECTRICITY 


the  required  units ;  and  sometimes  by  taking  a  series 
of  readings,  and  from  these  making  the  curve  that 
would  show  the  relation  of  the  deflection  to  the  required 
units. 

The  first  method  was  not  very  satisfactory,  since  the 
value  of  the  reduction  factor  in  one  part  of  the  scale  was 
often  different  from  its  value  in  another  part ;  while  the 
second  method  made  it  necessary  to  refer  constantly  to 
the  curve  of  the  instrument. 

In  order  to  obviate  these  difficulties  instruments  are 
now  made  direct-reading,  i.e.  they  are  so  calibrated  that 
the  divisions  of  the  scale  are  given  in  amperes  or  volts. 

EXPERIMENT  73.  —  To  calibrate  a  voltmeter  by  comparison  with  a 
standard  voltmeter. 

Apparatus. — A  standard  voltmeter ;  two  similar  rheostats;  cells; 
the  voltmeter  to  be  calibrated;  and  a  switch. 

Manipulation.  —  Couple  the  voltmeters  in  parallel  to  the  terminals 
of  one  of  the  rheostats,  and  put  both  the  rheostats  in  series  with  the 

cells  and  switch. 

There  should  be  a 
sufficient  number  of  cells 
to  give  a  full  deflection 
of  the  voltmeter  to  be 
calibrated.  A  dynamo 
can  be  substituted  if 
it  is  more  convenient. 
The  rheostats  should 
have  a  wide  range  of 
resistance  and  a  large 
number  of  steps. 

Beginning  with  the 
rheostat  arm  of  R  in 
the  position  of  maxi- 
mum resistance,  and  the  arm  of  R'  in  that  of  minimum,  send 
a  current  through  the  circuit  and  take  a  simultaneous  reading  of 
the  two  instruments.  Increase  the  resistance  in  one  rheostat  and 


FIG.  88 


THE  CALIBRATION   OF  INSTRUMENTS 


93 


diminish  it  in  the  other,  by  one  point  each,  and  take  'a  second  reading. 
Do  the  same  for  every  point  until  you  reach  the  full  deflection  of  the 
voltmeter  to  be  calibrated. 

This  experiment  gives  the  direct  method  of  comparison  that  would 
be  used  in  the  case  of  an  instrument  that  had  been  repaired  and 
needed  to  be  recalibrated.  If  the  instrument  is  a  voltmeter  the  scale 
of  which  is  in  degrees,  or  is  a  high-resistance  galvanometer  with  a 
similar  scale,  a  curve  should  be  made  showing  the  relation  between 
the  two  instruments  and  the  reduction  factor  found  for  the  different 
parts  of  the  scale. 

EXPERIMENT  74.  —  To  calibrate  a  high-resistance  galvanometer  by 
Ohm's  law. 

Apparatus.  —  An  ammeter;  switch;  two  similar  rheostats;  the 
galvanometer  to  be  calibrated ;  and  a  battery  capable  of  sending  a 
current  of  five  amperes  through  the  entire  resistance  of  one  rheostat. 

Manipulation.  —  Couple  the  apparatus  as  in  Fig.  89,  with  the  gal- 
vanometer placed  as  a  shunt  to  the  rheostat  /?,  the  resistance  of  which 
is  known  for  each  step.  Let 
the  rheostat  R'  be  an  exact 
duplicate  of  R  if  possible. 
Take  a  set  of  simultaneous 
readings  of  the  ammeter  and 
galvanometer,  beginning  with 
the  maximum  resistance  in  R 
and  the  minimum  resistance 
in  R'.  Move  the  arms  of  the 
rheostats  one  point  each  be- 
tween consecutive  readings. 
This  will  give  a  nearly  constant 
current  and  a  diminishing  fall 
of  potential  in  R,  with  a  corresponding  change  in  the  reading  of  the 
galvanometer.  Compute  the  values  of  the  potential  difference  at  the 
different  points  from  the  expression  E  =  CR,  and  make  the  calibration 
curve  of  the  galvanometer. 

EXPERIMENT  75.  —  To  calibrate  an  ammeter  by  comparison  with 
a  standard  ammeter. 

Apparatus. —  A  standard  ammeter;  switch;  battery;  rheostat;  and 
the  ammeter  to  be  calibrated. 


FIG. 


94 


ELECTRICITY 


Manipulation.  —  Couple  the   apparatus   as  in  Fig.  90  and  send  a 
current  through  the  circuit  when  the  rheostat  arm  is  in  such  a  posi- 
tion that  it  gives  the  minimum 

S  A  i  I     current.      Take    simultaneous 

readings  of  the  two  ammeters. 
Move  the  rheostat  arm  one 
step  and  repeat  the  readings. 
Do  the  same  for  every  step  of 
the  rheostat. 

Make  the  curve  for  the  in- 
strument and  find  the  reduc- 
FIG.  90  tion  factor. 

EXPERIMENT  76.  —  To  calibrate  a  low-resistance  galvanometer  by 
Ohm's  law. 

Apparatus.  —  Cells ;  rheostat ;  a  low-reading  voltmeter ;  switch ;  and 
the  galvanometer  to  be  calibrated. 

Manipulation.  —  Couple  the  apparatus  as  in  Fig.  91,  and  with  the 
resistance  of  the  rheostat  all 
in,  take  a  reading  of  the  two 
instruments.  Move  the  arm  of 
the  rheostat  one  step  at  a  time 
and  take  a  set  of  simultaneous 
readings. 

Make  the  curve  of  the  gal- 
vanometer, computing  the  cur- 
rents from  the  expression 

77* 

C  —  —'     In  this  expression,  J£ 

is  the  reading  of  the  voltmeter, 

and   R  is  the  resistance  of  the  galvanometer. 

QUESTIONS  AND  PROBLEMS 

1.  A  uniform  current  passing  for  12  min.  through  a  silver  vol- 
tameter increased  the  weight  of  the  negative  plate  by  6.84  g.     What 
was  the  current  in  amperes  ? 

2.  The  same  current  was   sent  through  a  copper  voltameter  for 
20  min.     How  much  copper  was  deposited? 

3.  A  potentiometer  wire,  1  m.  long,  has  5  cells  attached  at  its 
terminals.     There  is  no  deflection  of  the  galvanometer  when  the  key 


FIG.  91 


ELECTRICAL   INDUCTION  95 

connected  to  a  Clark  standard  cell  touches  the  wire  at  292.6  mm.  from 
one  end.     What  is  the  potential  difference  of  the  battery  pej  cell? 

4.  On  substituting  another  cell  for  the  standard,  the  new  position 
of  the  key  reads  387.7  cm.     What  is  the  E.  M.  F.  of  the  cell  ? 

5.  A  high-resistance  galvanometer  coupled  to  the  terminals  of  a 
coil  and  ammeter  placed   in   series   gave   a  deflection  of  55°.     The 
resistance  of  the  coil  being  12  ohms,  and  that  of  the  ammeter  being 
.2  ohm,  what  potential  difference  does  the  reading  indicate?     What  is 
the  reduction  factor  of  the  galvanometer  if  the  current  was  .5  ampere  ? 

80.  Electrical  Induction.  —  The  setting  up  of  a  current 
in  an  electrical  conductor  through  the  action  of  a  current 
in  a  neighboring  conductor  is  what  is  called  electrical  in- 
duction. The  physical  cause  for  the  production  of  this 
current  is  the  cutting  of  lines  of  magnetic  force  by  a  con- 
ductor. The  phenomena  have  various  forms,  but  they  can 
all  be  traced  to  this  one  cause.  It  is  immaterial  whether 
the  lines  of  force  are  cut  by  a  moving  conductor,  or 
whether  the  conductor  is  stationary  and  is  itself  cut  by 
the  moving  of  the  lines  of  force.  With  a  given  field  of 
force,  i.e.  one  with  a  certain  number  of 
lines  per  unit  area,  the  maximum  current 
is  induced  when  the  directions  of  the 
lines  of  force  and  the  conductor  are 
perpendicular  to  each  other. 

Since   a   current   is  induced   by   the 
cutting  of  the  lines  of  force  alone,  it  is 
evident  that  a  constant  current  flowing      X^^-zr^v 
in  a  circuit  will  not  induce  a  secondary 
current  in  a  stationary  conductor  near 
it.      If,  however,    we    consider   that 
current    is   increasing   from    zero   to 
maximum  and  coming  toward  the  ob- 

FIG.  92 

server,  as  indicated  in  A,  Fig.  92,  lines 

of  force  will  be  sent  out  from  it,  will  cut  conductor 


96  ELECTRICITY 

and  will  set  up  in  it  a  current  in  the  opposite  direction. 
The  amount  of  the  induction  will  depend  upon  the  inten- 
sity of  the  primary  current  in  A,  the  time  taken  by  the 
current  to  rise  from  zero  to  a  maximum,  and  the  distance 
between  the  conductors. 

If  now  the  current  in  A'  is  conceived  to  dimmish  to 
zero,  the  lines  of  force  will  contract  upon  A',  cutting  B'  in 
the  other  direction,  and  the  induced  current  will  be  in  the 
same  direction  as  the  primary. 

The  origin  of  the  lines  of  force  does  not  in  any  way 
affect  the  resulting  induction,  hence  induced  currents  can 
be  obtained  from  a  permanent  magnet. 

EXPERIMENT  77.  —  Induction  from  a  permanent  magnet. 

Apparatus.  —  A  cylindrical  permanent  magnet  about  18  in.  long; 
copper  wire  No.  30 ;  a  ballistic  galvanometer  or  millivoltmeter. 

Manipulation.  —  Wind  a  test  coil  of  fifty  or  a  hundred  turns  so 
that  it  will  slide  easily  over  the  magnet,  and  connect  its  terminals  to 
the  galvanometer.  Make  two  wooden  collars  that  will  fit  over  the 
magnet,  and  arrange  brass  screws  so  that  the  collars  can  be  fixed 
at  any  place  along  the  magnet.  Slide  the  test  coil  over  the  magnet 
and  fix  the  collars  2  in.  or  3  in.  apart  so  that  the  coil  can  be  dropped 
from  one  collar  to  the  other.  Observe  and  make  a  record  of  the  throw 
of  the  galvanometer  needle.  Move  the  collars  a  half  inch  and  repeat. 
Do  this  for  every  half  inch  over  the  entire  length  of  the  magnet. 

This  experiment  should  bring  out  the  facts  that  the  amount  of  the 
induction  depends  upon  the  number  of  lines  of  force  cut  in  a  given 
time,  i.e.  upon  the  rate  of  cutting  the  lines  of  force,  and  that  the  direc- 
tion of  the  current  induced  is  determined  by  the  direction  of  cutting 
of  the  lines  of  force.  Make  a  curve  in  which  the  distance  of  the 
middle  of  the  coil  from  one  end  shall  be  laid  off  along  the  vertical 
axis,  and  the  throw  of  the  needle  along  the  horizontal. 

EXPERIMENT  78.  —  The  induction  of  a  current  in  a  coil. 

Apparatus.  —  Copper  wire  Nos.  18  and  24;  spools  of  some  insu- 
lating material  with  an  inch  hole  in  them;  ballistic  galvanometer; 
ammeter ;  rheostat ;  cells ;  and  a  switch. 


ELECTRICAL  INDUCTION 


97 


Manipulation.  —  Wind  one  spool  with  wire  No.  18,  counting  the 
number  of  turns.  Wind  a  spool  with  the  No.  24  wire,  putting  on 
the  same  number  of  turns  as  on  the  first  spool.  Couple  the  spool  of 
No.  18  wire  (the  primary)  in 
series  with  the  cells,  rheostat, 
ammeter,  and  switch,  and 
the  secondary  to  the  gal- 
vanometer, as  in  Fig.  93. 

Send  a  current  through 
the  primary  circuit  with  all 
the  rheostat  resistance  in, 
and  read  the  throw  of  the 
galvanometer.  Read  the 
throw  on  breaking  the  circuit 
also,  and  keep  a  record.  Re- 
peat the  experiment  for  each 
step  of  the  rheostat  until  its 
resistance  is  all  out,  keeping 
the  record  on  both  the  "  make "  and  the  "  break "  of  the  circuit. 

Make  a  curve  having  for  horizontal  distances  the  current  in  the 
primary  and  for  vertical  distances  the  throw  of  the  needle.  It  will 
be  well  to  make  the  experiment  in  the  reverse  order;  i.e.  beginning 
with  the  last  reading  of  the  experiment,  go  over  each  step,  increasing 
the  resistance  until  the  maximum  is  reached.  Does  this  curve  coin- 
cide with  the  first? 


FIG.  S3 


EXPERIMENT  79. — The  induction  of  a  current  in  a  coil  with  an 
iron  core. 

Apparatus. — The  same  as  that  used  in  Experiment  78,  with  the 
addition  of  a  soft  iron  rod  an  inch  in  diameter  and  an  inch  longer 
than  the  combined  length  of  the  coils  used. 

Manipulation.  —  Thrust  the  iron  rod  through  the  coils  so  that  it 
will  extend  a  half  inch  on  each  side.  Repeat  the  experiment  in  the 
same  order  as  before  and  keep  a  record.  Repeat  the  experiment,  sub- 
stituting a  bundle  of  soft  iron  wires  for  the  iron  rod. 

Make  curves  of  the  results  on  the  same  sheet  that  the  curve  for  the 
previous  experiment  was  made  on,  using  a  different  colored  ink.  Do 
the  curves  coincide?  In  what  respects  do  they  differ?  What  is  the 
significance  of  these  differences? 

ELEC.   AND  MAG.  7 


98'  ELECTEICITY 

Tf  Fig.  94  represents  a  cross  section  through  the  axis  of  the  coils 

and  the  core,  it  will  be  seen  that 
since  the  coil  P  is  the  origin  of 
the  lines  of  force,  in  order  to  pass 
through  the  core  and  take  the 
position  indicated  they  must  cut 
each  turn  of  the  coil  S.  Hence 
the  total  E.  M.  F.  of  the  induction 
will  depend  upon  the  number  of 
turns  in  S,  as  well  as  upon  the 
number  of  lines  of  force. 

EXPERIMENT  80.  —  The  effect  of  increasing  the  turns  in  the  sec- 
ondary. 

Apparatus. —  The  same  as  that  used  in  the  preceding  experiment, 
with  the  addition  of  another  coil,  S',  of  No.  24  wire  of  double  the 
number  of  turns. 

Manipulation.  —  Repeat  Experiment  79,  substituting  coil  S'  for 
coil  S. 

Make  the  curve  for  this  experiment  and  compare  it  with  those 
previously  obtained. 

The  above  arrangement  is  practically  a  transformer,  and 
shows  that  if  V  represents  the  voltage  of  an  alternating 
current  applied  to  the  terminals  of  a  primary  coil,  and  V 
the  voltage  of  the  current  obtained  from  the  secondary,  the 
relation  between  them  will  be  expressed  by  the  proportion 
V:  V  =  T:Tf,  in  which  T  and  T'  are  the  number  of  turns 
in  the  primary  coil  and  in  the  secondary,  respectively. 

EXPERIMENT  81.  —  The  effect  of  increasing  the  amount  of  iron 
in  the  magnetic  circuit. 

Apparatus.  —  The  same  as  that  used  in  Experiment  78,  with  the 
addition  of  a  quantity  of  soft  iron  wire. 

Manipulation.  — Cut  the  wire  into  such  lengths  that  on  thrusting  it 
through  the  coils  the  ends  can  be  brought  over  the  outside  and  lapped 
over  each  other.  When  the  coils  have  been  entirely  filled  with  the 
wire  so  arranged,  repeat  Experiment  78. 

Make  the  curve  for  the  results  obtained  and  compare  it  with  the 


SELF-INDUCTION 


99 


others.  This  arrangement  provides  a  nearly  complete  iron  circuit  for 
the  magnetic  lines  and  reduces  the  magnetic  reluctance  of  the  circuit. 
Would  you  use  the  Wheatstone  bridge  to  measure  the  resistance  of  a 
coil  with  an  iron  core  ? 

81.  Self-induction.  —  We  have  seen,  in  Fig.  92,  that  an 
increasing  current  in  a  primary  wire  induces  a  current  in 
the  opposite  direction  in  a  secondary,  and  that  a  diminish- 
ing current  in  a  primary  induces  a  current  in  the  same 
direction  in  the  secondary.  The  same  phenomena  will 
take  place  between  any  two  wires  of  a  coil,  one  of  which 
may  be  considered  the  primary  and  the  other  the  secondary. 
This  means  that  the  influence  of  a  coil  upon  an  increasing 
current  passing  through  it  is  to  oppose  or  delay  its  passage, 
while  the  effect  upon  a  diminishing  current  is  to  aid  or 
prolong  its  passage.  This  is  called  self-induction^  and  its 
amount  in  any  case  depends  upon  the  number  of  turns  in 
the  coil  and  the  character  of  the  magnetic  circuit. 

EXPERIMENT  82.  —  The  effect  of  self-induction  in  a  coil. 

Apparatus.  —  A  spark  coil ;  cells ; 
ammeter;  lamp  board  or  water  rheostat ; 
and  a  knife  switch. 

Manipulation.  —  Measure  the  resist- 
ance of  the  spark  coil  and  arrange  the 
rheostat  so  that  its  resistance  shall  be 
the  same.  Couple  the  apparatus  as  in 
the  figure,  close  the  switch,  and  observe 
the  action  of  the  ammeter.  Open  the 
switch  and  observe  both  the  action  of 
the  ammeter  and  the  sparking  at  the 
switch.  Substitute  the  rheostat  for  the 
spark  coil  and  repeat  the  experiment. 

The  gradual  creeping  up  of  the  cur- 
rent when  it  is  sent  through  the  spark  Fio.  95 
coil,  and  the  increase,  giving  a  spark, 

when  the  current  is  broken,  show  conclusively  the  effect  of  self- 
induction  in  a  coil. 


100  ELECTEICITT 

This  effect  need  not  be  taken  into  account  in  work  with 
direct  currents,  but  is  of  great  importance  in  alternating 
work.  A  coil  can  be  wound  non-inductively  by  doubling 
the  wire  and  winding  from  the  middle,  thus  causing  the 
self-induction  of  one  half  to  neutralize  that  of  the  other. 

A  suitable  spark  coil  for  the  experiment  can  be  made 
by  winding  a  pound  or  two  of  No.  24  magnet  wire  on  a 
spool  having  a  bundle  of  iron  wire  for  a  core. 

82.  Electrical  Testing.  —  Testing  may  be  broadly  di- 
vided into  two  classes  :  first,  the  testing  of  manufactured 
apparatus  to  see  that  the  requirements  of  its  operation 
have  been  met ;  and,  second,  the  testing  for  faults  that 
have  developed  in  use,  or  what  is  generally  known  as 
"hunting  trouble." 

The  principles  brought  out  in  the  measurements  that 
have  been  considered  will  usually  apply  in  these  tests. 
Only  a  few  of  the  simpler  tests  that  may  be  made  in  the 
laboratory  will  be  taken  up. 

EXPERIMENT  83.  —  To  test  the  resistance  of  a  switch  contact. 

It  has  been  shown  in  Experiment  48  that  a  good  contact  is  of 
great  importance  in  an  electrical  circuit.  With  large  currents  a  poor 
contact  results  in  a  loss  of  power  and  a  heating  of  the  switch ;  with 
small  currents,  in  a  lack  of  uniformity  in  the  current.  This  test  is 
simply  the  measurement  of  a  small  resistance. 

Apparatus.  —  Ammeter ;  millivoltmeter ;  cells ;  and  the  switch  to 
be  tested. 

Manipulation.  —  Couple  the  cells,  ammeter,  and  switch  in  series, 
and  the  millivoltmeter  as  a  shunt  to  the  switch.  Compute  the  resist- 
ance by  the  fall  of  potential  method,  using  different  currents. 

Compare  the  resistances  of  different  kinds  of  switches. 

EXPERIMENT  84.  —  To  test  the  resistance  of  the  body. 

Apparatus. —  A  source  of  current  giving  from  50  to  150  volts;  a 
high-resistance  voltmeter;  a  pair  of  tubular  brass  handles  an  inch  in 
diameter;  and  a  switch. 


ELECTRICAL 


101 


Manipulation.  —  Couple  one  terminal  of  the  voltmeter  to  one  side 
of  the  generator  and  the  other  terminal  to  one  of  the  brass  handles. 
Connect  the  second  handle  to  the  other  side  of  the  generator,  with 
the  switch  in  the  circuit,  and  let  the  person  whose  resistance  is  to  be 
measured  take  a  firm  hold  of  both  handles.  Close  the  circuit  and 
take  a  reading  of  the  voltmeter.  Then,  as  in  Section  69,  the  resist- 
ance will  be  given  by  the  expression  R  =  I  — -  —  1  )r,  in  which  V'  is 

the  voltage  of  the  generator,  V"  is  the  reading  of  the  voltmeter,  and 
r  is  the  resistance  of  the  voltmeter. 

The  character  of  the  contact  between  the  hands  and  the  brass 
handles  has  a  great  influence  upon  the  amount  of  the  resistance. 
Make  the  experiment  first  with  the  hands  dry,  and  then  after  wetting 
them  with  salt  water  or  any  other  electrolytic  solution. 

EXPERIMENT  85.  —  To  test  a  lighting  circuit  for  a  ground. 

In  many  lighting  stations  it  is  the  custom  to  connect  two  incan- 
descent lamps  across  the  terminals  of  the  dynamo  and  permanently  to 
connect  some  point  between  them  to  the  earth,  as  shown  in  the  figure. 


These  lamps  must  each  require  half  the  potential  of  the  circuit,  e.g. 
on  a  110-volt  circuit  the  lamps  must  be  55  volt.  If  a  leak  develops  at 
some  point  on  the  line,  as  at  C,  the  current  that  escapes  through  it 
will  be  shunted  around  lamp  A,  which  will  become  dim.  If  the 
ground  is  on  the  negative  side  of  the  line,  lamp  B  will  grow  dim. 
The  resistance  of  the  ground  can  be  determined  as  follows : 


102  ELECTRICITY 

Apparatus.  —  The  line  to  be  tested ;  a  high-resistance  voltmeter. 
Manipulation.  —  If  the  ground  is  on  the  positive  side,  couple  the 

voltmeter  between  the  negative   terminal   and   the  water  pipes  of 

the  building.     Read  the  voltmeter  and  compute  the  resistance  as  in 

the  preceding  experiment. 

If  the  line  is  not  supplied  with  the  ground-test  lamps,  both  sides 

of  the  circuit  should  be  tested.     The  insulation  of  the  dynamo  can  be 

tested  in  the  same  way,  by  cutting  out  the  line  current  and  coupling 

the  voltmeter  between  one  terminal  of  the  dynamo  and  the  earth,  or 

any  part  of  the  frame  or  the  foundation. 

A  convenient  form  of  contact  point  for  the  voltmeter  is  shown  in 

Fig.  97.     This  consists  of  a  wooden  or  vulcanite  handle  with  a  brass 

rod  set  in  the  end  and  pointed 
like  a  scratch  awl.  A  nut, 
running  on  the  rod  near  the 
handle,  connects  a  flexible 
cord  to  one  terminal  of  the 
voltmeter.  .  By  means  of  a 

pair  of  these  points,  contact  can  be  made  where  only  a  small  part  of 

the  surface  is  exposed. 

EXPERIMENT  86.  —  To  test  for  faults  in  commutator  and  arma- 
ture. 

Apparatus.  —  A  low-reading  voltmeter  or  millivolt  meter;  a  source 
of  current;  and  the  armature  to  be  tested. 

Manipulation.  —  Couple  the  millivoltmeter  to  the  contact  points 
that  have  just  been  described  and  the  commutator  brushes  to  the 
source  of  the  current.  Send  a  heavy  current  through  the  armature 
and  touch  any  two  opposite  bars  of  the  commutator  with  the  points. 
Read  the  millivoltmeter.  Pass  around  the  commutator,  taking  the 
opposite  pairs  in  order. 

If  the  readings  are  not  practically  all  alike,  it  is  evidence  that  there 
is  a  fault  in  either  the  armature  or  the  commutator.  The  location  of 
the  fault  can  easily  be  made  by  taking  the  readings  with  the  contact 
points  placed  on  adjacent  commutator  bars  all  around  the  commutator. 

EXPERIMENT  87.  —  To  test  the  leakage  of  lines  of  force  around  a 
dynamo. 

Apparatus.  —  Storage  cells ;  ammeter ;  rheostat ;  insulated  copper 
wire;  a  millivoltmeter ;  switch;  and  the  dynamo  to  be  tested. 


ELECTRICAL   TESTING 


103 


Manipulation.  —  Couple  the  storage  cells  to  the  terminals  of  the 
field  winding  of  the  dynamo  to  be  tested,  with  the  switch,  rheostat, 
and  ammeter  in  the  circuit.  Wind  from  the  wire  a  test  coil  of  several 
turns  around  the  middle  of  the  field  coil,  at  B  in  the  figure.  Connect 
this  coil  to  the  millivoltmeter  and  throw  the  switch.  Read  the  throw 


FIG.  98 

of  the  needle,  and  if  it  is  not  great  enough,  either  increase  the  current 
in  the  field  coil,  or  increase  the  number  of  turns  in  the  test  coil.  Wind 
a  coil  of  the  same  number  of  turns  around  the  armature  at  C  and 
repeat.  Make  this  experiment  with  different  currents,  taking  the  read- 
ing on  both  the  "  make  "  and  the  "break,"  and  from  the  results  obtained 
compute  the  ratio  v  between  the  number  of  lines  of  force  generated  in 
the  field  core  and  the  number  sent  through  the  core  of  the  armature. 

The  ratio,  w,  determined  in  this  test  is  of  great  importance  in  the 
designing  of  a  dynamo.  In  the  study  of  a  dynamo  already  built  it  is 
also  of  importance  to  know  where  the  losses  occur.  For  this  purpose 
the  test  can  be  extended  by  winding  test  coils  of  the  same  number  of 
turns  at  different  places,  as  at  D,  E,  F,  etc.,  and  repeating  the  experi- 
ment. As  a  large  number  of  storage  cells  would  be  required  to  give 
the  requisite  voltage  for  the  terminals  of  the  field  coil,  a  second 
dynamo  of  the  same  voltage  as  the  first  is  frequently  used  to  excite 
the  field  coils. 


104  ELECTRICITY 

EXPERIMENT  88.  —  To  test  the  carrying  capacity  of  fuse  wire. 

Apparatus.  —  Ordinary  fuse  wire  of  which  the  commercial  rating  is 
known  ;  storage  cells  ;  ammeter ;  rheostat ;  fuse  block ;  and  a  switch. 

Manipulation.  —  Couple  the  cells,  which  should  be  capable  of  giving 
a  current  of  at  least  double  the  rated  capacity  of  the  fuse  wire,  in 
series  with  the  fuse  block,  ammeter,  rheostat,  and  switch.  Arrange 
the  rheostat  so  that  the  current  shall  be  the  same  as  the  rating  of  the 
fuse.  Turn  on  the  current  for  30  sec.  and  observe  the  effect  upon  the 
fuse.  Increase  the  current  by  moving  the  arm  of  the  rheostat  one  step 
and  again  send  the  current  through  the  circuit  for  30  sec.  Keep  in- 
creasing the  current  and  sending  it  through  the  circuit  until  the  fuse 
blows  within  the  30  sec. 

The  results  obtained  will  show  that  the  rating  of  fuses  must  be  con- 
sidered as  only  approximate.  If  the  experiment  is  extended  by  intro- 
ducing a  circuit  breaker  into  the  circuit,  the  relative  value  of  the  two 
methods  of  protecting  the  line  in  different  classes  of  work  can  be  con- 
clusively shown. 

EXPERIMENT  89.  —  To  test  the  influence  of  the  length  of  a  fuse 
wire  upon  its  carrying  capacity. 

Apparatus.  —  Fuse  blocks  of  different  sizes  and  the  apparatus  used 
in  the  preceding  experiment. 

Manipulation.  —  Find  the  fusing  load  of  the  shortest  wire,  then  of 
the  next,  and  so  on,  using  all  the  blocks. 

Make  a  curve  showing  the  relation  between  the  fusing  current  and 
the  length  of  the  fuse. 

The  character  of  the  contact  pieces  by  which  the  fuse  is  held, 
whether  heavy  or  light,  as  well  as  the  position  of  the  fuse,  i.e.  whether 
lying  directly  upon  the  block  or  free  from  it,  has  a  great  effect  upon 
the  current  that  the  fuse  will  carry. 

This  test  will  be  more  satisfactory  if 
made  by  using  a  set  of  fuses  mounted  as 
in  Fig.  99.  The  ends  of  the  fuses  are 
clamped  in  the  same  sized  terminals  taken 
from  fuse  blocks  and  mounted  on  strips  of 
wood  fastened  to  a  base  board  as  shown. 
In  this  method  of  support  the  differences 

of  length  are  easily  arranged  and  the  conditions  of  conduction  and 
radiation  are  the  same  in  all. 


APPENDIX 


TABLE  NO.  1 

DIMENSIONS  AND  RESISTANCE  OF  PURE  COPPER  WIRE 
Matthieson's  Standard  at  75°  F.    Sp.  Gr.  8.9. 


SIZE 

DIAMETER 
IN  MILS 

AREA  IN 
CIRCULAR  MILS 

OHMS  PER 
1000  FEET 

FEET  PER 
POUND 

000 

409.64 

167805.0 

.062 

1.97 

00 

364.80 

133079.4 

.078 

2.49 

0 

324.95 

105592.5 

.098 

3.13 

1 

289.30 

83694.2 

.124 

3.95 

2 

257.63 

66373.0 

.156 

4.99 

3 

229.42 

52634.0 

.197 

6.29 

4 

204.31 

41742.0 

.249 

7.93 

5 

181.94 

33102.0 

.314 

10.00 

6 

162.02 

26250.0 

.395 

12.61 

7 

144.28 

20816.0 

.499 

15.90 

8 

128.49 

16509.0 

.629 

20.05 

9 

114.43 

13094.0 

.793 

25.28 

10 

101.89 

10381.0 

1.000 

31.38 

11 

90.74 

8234.0 

1.261 

40.20 

12 

80.81 

6529.9 

1.590 

50.69 

13 

71.96 

5178.4 

2.005 

63.91 

14 

64.08 

4106.8 

2.591 

80.59 

15 

57.07 

3256.7 

3.115 

101.63 

16 

50.82 

2582.9 

4.019 

128.14 

17 

45.26 

2048.2 

5.068 

161.59 

18 

40.30 

1624.3 

6.391 

203.76 

105 


106 


APPENDIX 


TABLE   NO.   1  (Continued} 


SIZE 

DIAMETER 
IN  MILS 

AREA  IN 
CIRCULAR  MILS 

OHMS  PER 
1000  FEET 

FEET  PER 
POUND 

19 

35.39 

1252.4 

8.289 

264.26 

20 

31.96 

1021.5 

10.163 

324.00 

21 

28.46 

810.1 

12.815 

408.56 

22 

25.35 

642.7 

16.152 

515.15 

23 

22.57 

509.5 

20.377 

649.66 

24 

20.10 

404.0 

25.695 

819.21 

25 

17.90 

320.4 

32.400 

1032.96 

26 

15.94 

254.0 

40.468 

1302.61 

27 

14.20 

201.5 

51.519 

1642.55 

28 

12.64 

159.8 

64.966 

2071.22 

29 

11.26 

126.7 

81.921 

2611.82 

30 

10.03 

100.5 

103.300 

3293.97 

It  will  be  observed  in  the  above  table  that  the  ohms  per  1000  ft. 
and  the  feet  per  pound  double  with  every  third  size,  that  the  area  in 
circular  mils  is  divided  by  two  with  every  third  size,  and  that  the 
diameter  in  mils  is  divided  by  two  with  every  sixth  size. 

A  mil  is  one  one-thousandth  of  an  inch. 

A  circular  mil  is  the  area  of  a  circle  one  mil  in  diameter  =  .7854 
sq.  mil. 

TABLE  NO.  2 

THE  RELATIVE  RESISTANCE  OF  CHEMICALLY  PURE  SUBSTANCES 
FOR  THE  SAME  LENGTH  AND   CROSS  SECTION  AT  0°  CENTIGRADE 


Silver,  annealed 
Copper,  annealed     . 
Silver,  hard  drawn  . 
Copper,  hard  drawn 
Aluminum,  annealed 
Platinum,  annealed 
Iron,  annealed 
German  silver 
Mercury  . 


1.000 
1.063 
1.086 
1.086 
1.935 
6.022 
6.460 
13.92 
62.73 


APPENDIX 


107 


TABLE  NO.  3 
RELATIVE  PROPERTIES  OF  COPPER  AND  ALUMINUM 


COPPER 

ALUMINUM 

Specific  gravity     .        ...  ... 

8.93 

2.68 

Conductivity       ...        .         .         .       '* 

100.00 

63.00 

Weight  for  equal  conductivity 

100.00 

48.00 

Area  for  equal  conductivity  .... 

100.00 

160.00 

Diameter  for  equal  conductivity  . 

100.00 

126.04 

TABLE  NO.  4 

EQUIVALENTS 

1  horse-power  =  33,000  foot-pounds  per  minute. 
1  kilowatt  =  44,236  foot-pounds  per  minute. 
1  horse-power  =  746  watts. 
1  kilowatt  =  1.34  horse-power. 

1  B.  T.  U.  (British  Thermal  Unit)  =  772  foot-pounds. 
1  watt  =  44.236  foot-pounds  per  minute. 
1  horse-power  =  42.746  B.  T.  U.  per  minute. 
1  kilowatt  =  57.3  B.  T.  U.  per  minute. 


ANSWERS  TO   PROBLEMS 


Page  34.— 3.    .192.         7.    4.29.         8.    H:  H'  ::  259.21  :  324. 

Page  60.— 6.  15°  42'.  7.  .000345  volts.  9.  7.32  Ib.  if  the  sulphate 
is  in  the  dry  form,  but  if  it  is  in  the  usual  form  of  crystals  or  "blue 
stone,"  the  chemical  symbol  of  which  is  CuS04(5H20),  the  amount 
required  will  be  11.5  Ib. 

Page  86. —1.    10.33  ohms.  2.    135.19  ohms.  3.    .0728  ohms. 

4.    1.63  ohms.  5.    (a)  4.44  ohms,     (6)  10  ohms.  6.    .805  ohms. 

9.    (a)  24.4  ohms,        (6)  6.66  ohms.  10.    (a)  317423.3  ohms, 

(6)  1529295.77  ohms.       11.   233.5  legal  ohms,  232.84  international  ohms. 

Page  94.  —  1.   8.497  amp.  2.    3.36  g.  3.    .98  volt  per  cell. 

4.   1.9  volts.         5.    (a)  61  volts,     (6)  1.109. 


108 


INDEX 


A  tangent  position,  30. 
Ammeter,  denned,  53. 

calibration  of,  91-94. 
Ampere,  87,  46. 
Angle  of  dip,  20,  21. 
Anode,  80. 
Armature,  of  electro-magnet,  40. 

of  horseshoe  magnet,  7. 
Astatic  galvanometer,  48,  49. 

Ballistic  galvanometer,  52. 
Batteries,  54-60. 

internal  resistance  of,  76-78. 
B.  A.  Unit,  83. 

Calibration  of  instruments,  91-94. 
Cathode,  81. 
Cells,  54-60. 

electro-motive  force  of,  59,  60,  90. 

internal  resistance  of,  76-78. 
Clark  cell,  90. 
Closed-circuit  cell,  57. 
Crowfoot  cell,  56. 
Current,  87-89,  46. 

unit  of,  87. 

See  Electric  Current. 
Curve,  22. 

D'Arsonval  galvanometer,  50,  51. 
Deadbeat,  51. 
Declination,  24. 
Deflection,  law  of,  36. 
Demagnetization,  10-12,  9. 
Differential  galvanometer,  51,  52. 
method  of  measuring  .resistance, 

72,  73. 

Dipping  needle,  20,  23,  24. 
Direct-reading,  92. 

Distribution  of  magnetism,  along  2 
bar  magnet,  27. 


Dry  battery,  58. 
Dynamo,  tests  of,  102, 103. 

Earth's  magnetic  force,  8-10. 

components  of,  19,  20,  33. 
Edelmann  galvanometer,  49. 
Electric  bell,  41,  42. 
Electric  current,  46,  35,  36,  39. 

magnetic  effects  of,  35-39,  44,  45. 

measurement  of,  87-89. 

representation  of,  45. 
Electrical  contacts,  60,  61. 
Electrical  induction,  95-100. 
Electrical  resistance,  see  Resistance. 
Electrical  testing,  100-104. 
Electrode,  80. 
Electrolysis,  80. 
Electrolyte,  80. 

resistance  of,  80-82. 
Electrolytic  method  of  measuring  cur- 
rent, 88. 
Electro-magnets,  40. 

polarity  of,  39. 

uses  of,  40-43. 
Electro-motive  force,  46,  90,  91. 

unit  of,  89,  90. 

Fall  of  potential,  along  a  wire,  64,  65. 
method  of  measuringcurrent,  88, 89. 
method  of  measuring  resistance, 

65-S7. 
Figure  of  merit,  of  galvanometers,  52, 

53. 
Fuse  wire,  tests  of,  104. 

Galvanic  cell,  54. 
Galvanometers,  46-54. 

calibration  of,  93,  94. 

classes  of,  46,  47. 


109 


110 


INDEX 


Galvanometers,  controlling  force  of,  47. 

figure  of  merit  of,  52,  53. 

principles  of,  37,  38,  46. 
Graphical  method,  22. 
Gravity  cell,  55,  56,  90. 

Horizontal  component  of  earth's  mag- 
netism, 19,  20,  33. 
Horseshoe  magnet,  7. 
See  Magnets. 

Inclination,  of  earth's  magnetic  force, 

20,  21. 

Induction,  electrical,  95-100. 
Induction,  magnetic,  8. 

explanation  of,  16.  17. 

of  the  earth,  8-10. 
Insulation  resistance,  80. 
Internal  resistance  of  batteries,  76-78. 

Lamp  resistance  board,  85. 

Law  of  deflection,  36. 

Law  of  mutual  action,  7,  14. 

Law  of  polarity,  caused  by  current  in 

coil,  39,  44. 
Leclanche  cell,  56,  57. 
Lines  of  magnetic  force,  12-15. 

around  a  conductor,  44,  45. 

construction  of  direction,  14,  15. 

induction  caused  by  cutting  of,  95- 
99. 

Magnet.    See  Magnets. 
Magnetic  couple,  of  earth,  19. 
Magnetic  declination,  24-26. 
Magnetic  effects  of  electric  current, 

35-39,  44,  45,  95-99. 
Magnetic  field,  12. 

intensity  of,  27. 
Magnetic  induction,  8-10. 

explanation  of,  16,  17. 
Magnetic  lines  of  force,  12-15,  44,  45, 

95-99. 

Magnetic  meridian,  7,  8. 
Magnetic  moment,  of  needle,  19. 

of  magnet,  30,  33,  34. 
Magnetic  needle,  6. 

action  of  a  magnet  upon,  27-31. 

action  of  earth  upon,  18,  19. 

deflected  by  current  near,  36,  37. 


Magnetic  needle,  how  to  make,  6, 10. 

magnetic  moment  of,  19. 

vibration  of,  27,  28,  31-33. 

See  Magnets. 

Magnetic  poles,  of  earth,  8. 
Magnetic  substances,  5. 
Magneto,  43. 
Magnetometer,  31. 
Magnets,  5-7. 

action  on  a  needle,  27-31. 

bar,  6. 

demagnetized  by  heat,  11,  12. 

distribution  of  magnetism,  27,  28. 

effect  of  breaking,  15,  1G. 

effect  on  a  needle,  27-31. 

horseshoe,  7. 

how  to  make,  9,  10. 

lifting  power  of,  17,  18. 

lines  of  force  of,  12-15. 

magnetic  moment  of,  30,  33,  34. 

moment  of  inertia  of,  31,  32. 

mutual  action  of,  7,  14. 

poles  of,  6,  7,  23. 

vibration  of,  31-33. 

See  Magnetic  Needle. 
Mance's  method  of  measuring  inter- 
nal resistance,  76,  77. 
Measurement,  of  current,  88,  89. 

of  electro-motive  force,  90,  91. 

of  inclination  of  earth's  magnetic 
force,  20,  21. 

of  magnetic  declination,  24-26. 

of  magnetic  intensity,  27. 

of  magnetic  moment,  19,  30,  33. 

of  potential  difference,  91. 

of  resistance,  64-83,  100-102. 
Moment  of    inertia,    of    magnet,  31, 
32. 

Nil  method,  48. 
Non-inductive  coil,  76,  100. 
North  pole,  7. 
North  star,  24-26. 

Oersted's  experiment,  35,  36. 
Ohm,  unit  of  resistance,  82,  83,  46. 
Ohm's  law,  62,  63. 

in  measurement  of  potential  differ- 
ence, 91. 
Open-circuit  cell,  57. 


INDEX 


111 


Parallel  circuits,  resistance  of,  73-75. 
Parallel  coupling  of  cells,  37. 
Plunge  battery,  58. 
Polaris,  24-26. 
Polarity,  test  of,  9. 

law  of,  in  electro-magnets,  39. 
Polarized  bell,  42-44. 
Poles  of  a  magnet,  6,  7. 

found  by  dipping  needle,  23,  24. 

found  by  method  of  vibrations.27,28. 
Portable  testing  set,  70-72. 
Potassium  bichromate  cell,  57,  58. 
Potential  difference,  measurement  of, 

91. 

Potentiometer,  90. 
Primary,  96,  97. 

Reflecting  galvanometer,  49. 
Relay,  40. 
Resistance,  60-86,  46. 

affected  by  temperature,  78,  79. 

battery,  internal,  76-78. 

boxes,  63. 

formula  for,  62. 

measurement  of,  64-83. 

of  electric  lights,  79. 

of  electrolytes,  80-82. 

of  a  ground,  101,  102. 

of  human  body,  100,  101. 

of  insulation,  80. 

of  parallel  circuits,  73-75. 

of  switch  contact,  100. 

specific,  62. 


Resistance,  tables  of,  105,  106. 

unit  of,  82,  83. 
Rheostats,  83-86. 

Secondary,  95,  97. 
Self-induction,  99,  100. 
Series  coupling  of  cells,  37. 
Shunts,  75,  76. 
Siemens  unit,  83. 
Solenoid  galvanometer,  37,  38. 
Sounder,  40. 
South  pole,  7. 
Specific  resistance,  62. 
Substitution  method  of  measuring  re- 
sistance, 64. 

Tangent  galvanometer,  47,  48. 
Telegraph,  40,  41. 
Temperature  coefficient,  78. 
Testing  set,  portable,  70-72. 
Thomson  galvanometer,  49. 
Throw  of  galvanometer  needle,  52. 
Transformer,  98. 

Volt,  46,  89,  90. 
Voltaic  cell,  54. 
Voltameter,  88. 
Voltmeters,  53,  54. 
calibration  of,  91-93. 

Wheatstone  bridge,  67-71. 
Zero  method,  49. 


A  Brief  Course  in  General  Physics 

Experimental  and  Applied 

BY  GEORGE  A.    HOADLEY,   A.M.,   C.E. 
Professor  of  Physics  in  Swarthmore  College. 

Cloth,  12mo,  463  pages.     Fully  illustrated  .      '.-       .     $1.20 


This  Brief  Course  in  General  Physics  is  designed  to 
provide  a  text-book  for  High  Schools  and  other  Second- 
ary Schools  that  can  be  completed,  with  a  reasonable 
amount  of  work,  within  an  academic  year.  In  its  prepara- 
tion the  author's  aim  has  been  to  present  the  essential 
facts  and  phenomena  of  physics  in  a  clear  and  concise 
manner,  and  in  such  a  way  as  to  awaken  the  interest  of 
the  student  in  the  subjects  treated,  and  by  awakening  this 
interest  to  secure  familiarity  with  the  action  of  physical 
forces,  and  the  laws  which  govern  those  forces. 

The  book  is  constructed  on  the  principle  that  to  in- 
sure the  greatest  benefit  from  the  study  of  Physics,  there 
should  be  a  coordination  of  (i)  a  reliable  text,  (2)  class 
demonstrations  of  stated  laws,  (3)  practical  questions  and 
problems  on  the  application  of  these  laws,  and  (4)  per- 
sonal experimentation  in  the  laboratory. 


Copies  of  the  book  -will  be  sent,  prepaid,  on  receipt  of  tht  price. 

American   Book  Company 

New  York  •  Cincinnati  •  Chicago 

(159) 


LOWER  DIVISION 


328841 


LOWER  DIVISION 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


